Deck 38:Vectors in the Plane

Question 1

Find a unit vector in the direction of the given vector.? $\mathbf { w } = 5 \mathbf { j }$ ?

A)j
B)i
C)- j
D)- i
E)?i - j

Answer 1

j

Question 2

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ?
Magnitude
Angle $\| \mathbf { v } \| = 4$ 0°
?
?

A) $\langle 0,0 \rangle$
B)? $\langle 4,4 \rangle$
C)? $\langle 0,4 \rangle$
D)? $\langle 4,0 \rangle$
E)? $\langle - 4,0 \rangle$

Answer 2

? $\langle 4,0 \rangle$

Question 3

Find 2u - 3v.? $\mathbf { u } = 4 \mathbf { i } , \mathbf { v } = 5 \mathbf { j }$ ?

A)? $15 \mathbf { i } - 8 \mathbf { j }$
B) $4 \mathbf { i } - 5 \mathbf { j }$
C) $- 8 \mathbf { i } - 15 \mathbf { j }$ ?
D) $8 \mathbf { i } - 15 \mathbf { j }$
E) $8 \mathbf { i } + 15 \mathbf { j }$ ?

Answer 3

$8 \mathbf { i } - 15 \mathbf { j }$

Question 4

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place. ) ​

A)Vertical ≈ 118.6 ft/sec,Horisontal ≈ 1,695.9 ft/sec.
B)​Vertical ≈ 119.6 ft/sec,Horisontal ≈ 1,696.9 ft/sec.
C)​Vertical ≈ 1,695.9 ft/sec,Horisontal ≈ 1,695.9 ft/sec.
D)​Vertical ≈ 1,695.9 ft/sec,Horisontal ≈ 118.6 ft/sec.
E)​Vertical ≈ 118.6 ft/sec,Horisontal ≈ 118.6 ft/sec.

Question 5

Find u + v.? $\mathbf { u } = \langle - 5,3 \rangle , \mathbf { v } = \langle 0,0 \rangle$ ?

A)? $$\langle - 4,4 \rangle$$
B) $\langle - 5 , - 5 \rangle$ ?
C)? $\langle 3,3 \rangle$
D)? $\langle - 5,3 \rangle$
E)? $\langle 3 , - 5 \rangle$

Question 6

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ?
Magnitude
Angle $\| \mathbf { v } \| = 6$ $45 ^ { \circ }$ ?

A)? $\langle - 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$
B)? $\langle - 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$
C)? $\langle 3,3 \rangle$
D)? $\langle 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$
E)? $\langle 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$

Question 7

Find a unit vector in the direction of the given vector. ?? $\mathbf { u } = \langle 4,0 \rangle$ ?

A) $\langle 1,1 \rangle$
B) $\langle 1,0 \rangle$
C) $\langle 0,0 \rangle$
D) $\langle 4,0 \rangle$
E) $\langle 0,1 \rangle$

Question 8

Find a unit vector in the direction of the given vector.? $\mathbf { u } = \langle 0 , - 4 \rangle$ ?

A)? $\langle - 1 , - 1 \rangle$
B)? $\langle - 1,0 \rangle$
C)? $\langle 0,0 \rangle$
D) $\langle 0 , - 1 \rangle$
E)? $\langle 1,0 \rangle$

Question 9

Find a unit vector in the direction of the given vector.? $\mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j }$ ?

A)? $- \frac { \sqrt { 2 } } { 2 } \mathbf { i } - \frac { \sqrt { 2 } } { 2 } j$
B)? $- \frac { \sqrt { 2 } } { 2 } \mathbf { i } + \frac { \sqrt { 2 } } { 2 } j$
C)? $\frac { \sqrt { 2 } } { 2 } \mathbf { i } - \frac { \sqrt { 2 } } { 2 } \mathbf { j }$
D)? $\sqrt { 2 } \mathbf { i } + \sqrt { 2 } \mathbf { j }$
E) $\frac { \sqrt { 2 } } { 2 } \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j }$

Question 10

Find 2u - 3v.? $\mathbf { u } = 6 \mathbf { i } , \mathbf { v } = \mathbf { j }$ ?

A) $12 \mathbf { i } - 3 \mathbf { j }$
B)? $- 12 \mathbf { i } - 3 \mathbf { j }$
C)? $6 \mathbf { i } - 3 \mathbf { j }$
D)? $12 \mathbf { i } + 3 \mathbf { j }$
E)? $6 i - j$

Question 11

Find u - v.? $\mathbf { u } = \langle 0,0 \rangle , \mathbf { v } = \langle 2,1 \rangle$ ?

A)? $\langle - 1 , - 2 \rangle$
B)? $\langle - 1 , - 1 \rangle$
C) $\langle - 2 , - 1 \rangle$
D)? $\langle - 2 , - 2 \rangle$
E)? $\langle - 1,0 \rangle$

Question 12

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal,find the vertical and horizontal components of the velocity.(Round your answers to one decimal place. ) ​

A)Vertical ≈ -55.7 mi/h,Horisontal ≈ 91.7 mi/h.
B)Vertical ≈ 90.7 mi/h,Horisontal ≈ -56.7 mi/h.
C)Vertical ≈ -56.7 mi/h,Horisontal ≈ -56.7 mi/h.
D)Vertical ≈ -56.7 mi/h,Horisontal ≈ 90.7 mi/h.
E)Vertical ≈ 90.7 mi/h,Horisontal ≈ 90.7 mi/h.

Question 13

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. ​
Initial Point
Terminal Point
(0,-8)
​(9,12)
​
​

A)​9i + 20j
B)​-9i - 20j
C)​20i - 9j
D)​​20i + 9j
E)​9i - 20j

Question 14

Find u + v.? $\mathbf { u } = \langle 4,5 \rangle , \mathbf { v } = \langle 6,0 \rangle$ ?

A)? $\langle 10,10 \rangle$
B)? $\langle 11,6 \rangle$
C)? $\langle 5,5 \rangle$
D)? $\langle 5,10 \rangle$
E) $\langle 10,5 \rangle$

Question 15

Find a unit vector in the direction of the given vector.? $\mathbf { u } = \langle - 6,6 \rangle$ ?

A) $\langle 0,0 \rangle$
B)? $\left\langle - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$
C)? $\left\langle - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$
D)? $\left\langle \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right\rangle$
E)? $\left\langle \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right\rangle$

Question 16

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point
Terminal Point
(-9,9)​
​(10,-10)

A)19i - 19j
B)​-19i + 19j
C)​​-19i - 19j
D)​19i + 19j
E)​-19i - 19j

Question 17

Find the component form and the magnitude of the vector v. Initial Point
Terminal Point
(1,3)
(-8,-9)

A) $\mathbf { v } = \langle 1 , - 8 \rangle ; \| \mathbf { v } \| = 15$
B) $\mathbf { v } = \langle - 9 , - 12 \rangle ; \| \mathbf { v } \| = 8$
C)? $\mathbf { v } = \langle - 9 , - 12 \rangle ; \| \mathbf { v } \| = 15$
D)? $\mathbf { v } = \langle - 8 , - 9 \rangle ; \| \mathbf { v } \| = 12$
E)? $\mathbf { v } = \langle 1 , - 8 \rangle ; \| \mathbf { v } \| = 8$

Question 18

Find u - v.? $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } , \mathbf { v } = 4 \mathbf { j }$ ?

A)? $- 2 \mathbf { i } - 2 \mathbf { j }$

B)? $- 3 \mathbf { i } - 2 \mathbf { j }$ .

C)? $- 2 \mathbf { i } - 2 \mathbf { j }$ .

D)? $2 \mathbf { i } - 2 \mathbf { j }$ .

E)? $\mathrm { i } - \mathrm { j }$

Question 19

Find u - v.? $\mathbf { u } = \mathbf { i } + \mathbf { j } , \mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j }$ ?

A)?-i - 4j
B)-2i - 4j
C)-i + 4j
D)-2i + 4j
E)-i + 5j

Question 20

Find u + v.? $\mathbf { u } = \langle 6,1 \rangle , \mathbf { v } = \langle 1,7 \rangle$ ?

A)? $\langle 8,9 \rangle$
B) $\langle 7,8 \rangle$
C)? $\langle 8,8 \rangle$
D)? $\langle 8,7 \rangle$
E)? $\langle 7,7 \rangle$

Question 21

Let w be a vector with initial point (4,-4)and terminal point (2,5).Write w as a linear combination of the standard unit vectors i and j.

A)? $\mathbf { w } = 8 \mathbf { i } - 3 \mathbf { j }$
B)? $\mathbf { w } = 0 \mathbf { i } + 3 \mathbf { j }$
C)? $\mathbf { w } = \mathbf { i } + 6 \mathbf { j }$
D)? $\mathbf { w } = - 2 \mathbf { i } + 9 \mathbf { j }$
E)? $\mathbf { w } = 6 \mathbf { i } - 9 \mathbf { j }$

Question 22

?Find a unit vector in the direction of $\mathbf { u } = 4 \mathbf { i } - 2 \mathbf { j }$ . ?

A)? $\left\langle - \frac { 2 \sqrt { 5 } } { 5 } , \frac { \sqrt { 5 } } { 5 } \right\rangle$
B)? $\left\langle \frac { 4 \sqrt { 5 } } { 5 } , - \frac { 2 \sqrt { 5 } } { 5 } \right\rangle$
C)? $\left\langle \frac { 8 \sqrt { 5 } } { 5 } , - \frac { 4 \sqrt { 5 } } { 5 } \right\rangle$
D)? $\left\langle \frac { 2 \sqrt { 5 } } { 5 } , - \frac { 2 \sqrt { 5 } } { 5 } \right\rangle$
E)? $\left\langle \frac { 2 \sqrt { 5 } } { 5 } , - \frac { \sqrt { 5 } } { 5 } \right\rangle$

Question 23

?Find the magnitude of vector v with initial point (7,5)and terminal point (-3,-5). ?

A)? $10 \sqrt { 2 }$
B)?14
C)? $20 \sqrt { 2 }$
D)? $\sqrt { 74 }$
E)? $2 \sqrt { 51 }$

Question 24

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.
​

A)2,761.4 lb
B)2,764.4 lb
C)2,763.4 lb
D)2,765.4 lb
E)2,762.4 lb

Question 25

A loaded barge is being towed by two tugboats,and the magnitude of the resultant is 6,400 pounds directed along the axis of the barge (see figure).Find the tension in the tow lines if they each make an angle 21° with the axis of the barge.Approximate the answer to one decimal place.​ ​ where a = 21°.

A)3,425.7 lb
B)3,429.7 lb
C)3,426.7 lb
D)3,428.7 lb
E)3,427.7 lb

Question 26

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.
​

A)18.1 lb
B)21.1 lb
C)19.1 lb
D)20.1 lb
E)17.1 lb

Question 27

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place.​ ​

A)​​T_L = 12.7 lb;TR = 12.7 lb
B)​T_L = 11.9 lb;TR = 11.9 lb
C)​T_L = 11.9 lb;TR = 12.7 lb
D)T_L = 12.7 lb;TR = 11.9 lb
E)​​T_L = 13.7 lb;TR = 12.9 lb

Question 28

Using the figure below,sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.]? $-u$ ?

A)?
B)?
C)?
D)?
E)none of these

Question 29

The initial and terminal points of vector v are (3,-8)and (7,1),respectively.Select v in component form. ?

A)? $\mathbf { v } = \langle - 4 , - 9 \rangle$
B)? $\mathbf { v } = \langle - 4,9 \rangle$
C) $\mathbf { v } = \langle 4,9 \rangle$
D) $\mathbf { v } = \langle 4 , - 9 \rangle$
E)? $\mathbf { v } = \langle 9,4 \rangle$

Question 30

Find the magnitude of vector v.?

A) $\| \mathbf { v } \| = 5$
B)? $\| \mathbf { v } \| = 2 \sqrt { 7 }$
C)? $\| \mathbf { v } \| = 6$
D)? $\| \mathbf { v } \| = 4 \sqrt { 2 }$
E)? $\| \mathbf { v } \| = 6 \sqrt { 3 }$

Question 31

Find the component form of vector v. ?? ?

A) $\mathbf { v } = \langle 4 , - 5 \rangle$
B)? $$\mathbf { v } = \langle - 4 , - 5 \rangle$$
C)? $\mathbf { v } = \langle 4 , - 3 \rangle$
D)? $$\mathbf { v } = \langle 5,4 \rangle$$
E)? $\mathbf { v } = \langle - 5,4 \rangle$

Question 32

Given $$\mathbf { u } = \langle 3 , - 2 \rangle$$ and $\mathbf { v } = \langle - 3,2 \rangle$ ,determine $- 4 \mathbf { u } - \mathbf { v }$ .

A)? $$- 4 \mathbf { u } - \mathbf { v } = \langle 9 , - 14 \rangle$$
B) $- 4 \mathbf { u } - \mathbf { v } = \langle - 9,6 \rangle$
C)? $- 4 \mathbf { u } - \mathbf { v } = \langle - 14 , - 14 \rangle$
D)? $- 4 \mathbf { u } - \mathbf { v } = \langle 11 , - 14 \rangle$
E)? $- 4 \mathbf { u } - \mathbf { v } = \langle - 11,10 \rangle$

Question 33

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. ​​ ​
Where b = 28°
​

A)18.0 lb
B)17.0 lb
C)16.0 lb
D)19.0 lb
E)15.0 lb

Question 34

?Find the vector v that has a magnitude of 9 and is in the same direction as u,where $\mathbf { u } = \langle 6 , - 5 \rangle$ . ?

A)? $\mathbf { v } = \left\langle \frac { 5 \sqrt { 61 } } { 61 } , - \frac { 6 \sqrt { 61 } } { 61 } \right\rangle$
B)? $\mathrm { v } = \left\langle \frac { 45 \sqrt { 61 } } { 61 } , - \frac { 54 \sqrt { 61 } } { 61 } \right\rangle$
C)? $\mathbf { v } = \left\langle \frac { \sqrt { 61 } } { 61 } , - \frac { \sqrt { 61 } } { 61 } \right\rangle$
D)? $\mathbf { v } = \left\langle \frac { 6 \sqrt { 61 } } { 61 } , - \frac { 5 \sqrt { 61 } } { 61 } \right\rangle$
E)? $\mathbf { v } = \left\langle \frac { 54 \sqrt { 61 } } { 61 } , - \frac { 45 \sqrt { 61 } } { 61 } \right\rangle$

Question 35

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.
​

A)19.4°
B)​21.4°
C)​23.4°
D)​20.4°
E)​22.4°

Question 36

Find the component form of vector v with initial point (1,-7)and terminal point (-3,1).

A)? $\mathbf { v } = \langle - 4 , - 8 \rangle$
B) $\mathbf { v } = \langle - 4,8 \rangle$
C)? $v = \langle 8 , - 4 \rangle$
D)? $v = \langle 0 , - 4 \rangle$
E)? $\mathbf { v } = \langle - 8 , - 4 \rangle$

Question 37

?Find a unit vector in the direction of $\mathbf { w } = \langle - 4 , - 6 \rangle$ . ?

A)? $\left\langle - \frac { 2 \sqrt { 13 } } { 13 } , - \frac { 3 \sqrt { 13 } } { 13 } \right\rangle$
B)? $\left\langle - \frac { \sqrt { 13 } } { 39 } , - \frac { \sqrt { 13 } } { 26 } \right\rangle$
C)? $\left\langle - \frac { \sqrt { 13 } } { 4 } , - \frac { \sqrt { 13 } } { 6 } \right\rangle$
D)? $\left\langle - \frac { \sqrt { 13 } } { 13 } , - \frac { \sqrt { 13 } } { 13 } \right\rangle$
E)? $\left\langle - \frac { 8 \sqrt { 13 } } { 13 } , - \frac { 12 \sqrt { 13 } } { 13 } \right\rangle$

Question 38

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.
​

A)1,812.8 lb
B)1,810.8 lb
C)1,814.8 lb
D)1,811.8 lb
E)1,813.8 lb

Question 39

Given $\mathbf { u } = 5 \mathbf { i } - 3 \mathbf { j }$ and $\mathbf { v } = \mathbf { i } + 2 \mathbf { j }$ ,determine $9 \mathbf { u } - 3 \mathbf { v }$ .

A)? $9 \mathbf { u } - 3 \mathbf { v } = 39 \mathrm { i } - 39 \mathrm { j }$
B)? $9 \mathbf { u } - 3 \mathbf { v } = 3 \mathbf { i } + 3 \mathbf { j }$
C)? $9 \mathbf { u } - 3 \mathbf { v } = 42 \mathbf { i } - 33 \mathbf { j }$
D)? $9 \mathbf { u } - 3 \mathbf { v } = - 6 \mathbf { i } + 39 \mathbf { j }$
E)? $9 \mathbf { u } - 3 \mathbf { v } = - 30 \mathbf { i } + 39 \mathbf { j }$

Question 40

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point
Terminal Point
(-9,7)
​(0,2)
​

A)-9i - 5j
B)​-5i + 9j
C)​​-5i ​- 9j
D)​9i - 5j
E)​9i + 5j

Question 41

Given that Force 1 = 55 pounds and Force 2 = 130 pounds,find the angle between the forces if the magnitude of the resultant force is 120 pounds.Round your answer to the nearest degree. ​

A)72°
B)59°
C)67°
D)79°
E)64°

Question 42

?If $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$ and $\mathbf { v } = - 6 \mathbf { i } + 5 \mathbf { j }$ ,find $\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }$ .

A)? $\mathbf { w } = - 39 \mathbf { i } + 43 \mathbf { j }$
B)? $\mathbf { w } = - 33 \mathbf { i } + 43 \mathbf { j }$
C)? $\mathbf { w } = - 27 \mathbf { i } + 55 \mathbf { j }$
D)? $\mathbf { w } = - 39 \mathbf { i } + 45 \mathbf { j }$
E)? $\mathbf { w } = 16 \mathbf { i } - 12 \mathbf { j }$

Question 43

If $\| \mathbf { u } \| = 4$ and $\| \mathbf { v } \| = 6$ ,and the vectors make angles of 140° and 20° with the x-axis respectively,find the component form of the sum of u and v.Round answers to two decimal places.

A) $\langle 2.57,4.62 \rangle$
B)? $\langle - 0.84,5.22 \rangle$
C)? $\langle - 8.7,0.52 \rangle$
D)? $\langle 8.21 , - 1.01 \rangle$
E)? $\langle - 3.07 , - 5.12 \rangle$

Question 44

Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 30°.

A)? $\langle 4 \sqrt { 3 } , 4 \rangle$
B)? $\langle 4,4 \sqrt { 3 } \rangle$
C)? $\langle 8,8 \sqrt { 3 } \rangle$
D)? $\langle 8 \sqrt { 3 } , 8 \rangle$
E)? $\langle 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$

Question 45

?Find the magnitude and direction angle of $\mathbf { v } = - 2 \mathbf { i } - 6 \mathbf { j }$ .Round the direction angle to the nearest degree.

A)??||v|| = $3 \sqrt { 7 }$ ;? = 269°
B)??||v|| = $\sqrt { 30 }$ ;? = 239°
C)??||v|| = $2 \sqrt { 13 }$ ;? = 260°
D)?||v|| = $2 \sqrt { 10 }$ ;? = 252°
E)??||v|| = $\sqrt { 67 }$ ;? = 279°

Question 46

Find the magnitude and direction angle of $\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)$ .

A)? $\| \mathbf { v } \| = \sqrt { 6 } ; \theta = 80 ^ { \circ }$
B)? $\| \mathbf { v } \| = 6 ; \theta = 100 ^ { \circ }$
C)? $\| \mathbf { v } \| = 6 ; \theta = 80 ^ { \circ }$
D)? $\| \mathbf { v } \| = 6 ; \theta = 10 ^ { \circ }$
E)? $\| \mathbf { v } \| = \sqrt { 6 } ; \theta = 100 ^ { \circ }$

Question 47

Three forces with magnitudes of 74 pounds,98 pounds,and 105 pounds act on an object at angles 170°,220°,and 330°,respectively,with the positive x-axis.Find the magnitude and direction of the resultant force.Round answers to two decimal places.

A)99.08 pounds;240.95°
B)99.08 pounds;60.95°
C)117.42 pounds;240.95°
D)139.13 pounds;272.47°
E)117.42 pounds;60.95°

Question 48

Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 60°.

A)? $\langle 4 \sqrt { 3 } , 4 \rangle$
B)? $\langle 8,8 \sqrt { 3 } \rangle$
C) $\langle 4,4 \sqrt { 3 } \rangle$
D)? $\langle 8 \sqrt { 3 } , 8 \rangle$
E)? $\langle 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$

Question 49

Find the component form of v if $\| \mathbf { v } \| = 10$ and the angle it makes with the x-axis is 120°.

A)? $\langle - 5 \sqrt { 3 } , 5 \rangle$
B)? $\langle - 5 \sqrt { 3 } , - 10 \rangle$
C)? $\langle - 5 \sqrt { 2 } , 5 \sqrt { 2 } \rangle$
D)? $\langle - 5,5 \sqrt { 3 } \rangle$
E)? $\langle - 10,10 \sqrt { 3 } \rangle$

Question 50

Find the component form of v if $\| \mathbf { v } \| = 6$ and the angle it makes with the x-axis is 150°.

A)? $\langle - 6 \sqrt { 3 } , - 6 \rangle$
B)? $\langle - 6,6 \sqrt { 3 } \rangle$
C)? $\langle - 3 \sqrt { 3 } , 3 \rangle$
D)? $\langle - 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$
E)? $\langle - 3,3 \sqrt { 3 } \rangle$