Question 1

Find the component form of the indicated vector.&#10;

Accepted Answer

To find $7 \mathbf { u }$, multiply each component of $\mathbf { u } = \langle 4 , - 2 \rangle$ by 7, resulting in $\langle 28 , - 14 \rangle$.

Question 2

Find the component form and magnitude of the indicated vector.&#10;

Accepted Answer

The component form of $\overrightarrow{\mathrm{PQ}}$ is found by subtracting the coordinates of P from Q: $(-2 - (-1), 10 - 7) = (-1, 3)$. The magnitude is $\sqrt{(-1)^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10}$.

Question 3

R = (4, 5), S = (8, 8), O = (5, 6), and P = (9, 9)&#10;A) No&#10;B) Yes

Accepted Answer

To prove that $ \overrightarrow{R S} $ and $ \overrightarrow{O P} $ represent the same vector, we calculate the components of each vector. For $ \overrightarrow{R S} $, the components are $ S - R = (8 - 4, 8 - 5) = (4, 3) $. For $ \overrightarrow{O P} $, the components are $ P - O = (9 - 5, 9 - 6) = (4, 3) $. Since both vectors have the same components, they represent the same vector.

Question 4

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 5

Find the component form of the indicated vector.&#10;

Accepted Answer

To find $\mathbf { v } - \mathbf { u }$, subtract the components of $\mathbf { u }$ from $\mathbf { v }$: $\langle 1 - (-7), 9 - (-3) \rangle = \langle 8, 12 \rangle$.

Question 6

Find the component form and magnitude of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form and magnitude of...

Question 7

R = (4, 3), S = (13, 11), O = (0, 0), and P = (9, 8)&#10;A) No&#10;B) Yes

Accepted Answer

To prove that $ \overrightarrow{R S} $ and $ \overrightarrow{O P} $ represent the same vector, we calculate the components of each vector. For $ \overrightarrow{R S} $, the vector components are found by subtracting the coordinates of R from S, resulting in $ \overrightarrow{R S} = S - R = (13 - 4, 11 - 3) = (9, 8) $. For $ \overrightarrow{O P} $, since O is the origin (0, 0), the vector is simply the coordinates of P, which are (9, 8). Since both vectors have the same components, $ \overrightarrow{R S} = \overrightarrow{O P} = (9, 8) $, proving they represent the same vector.

Question 8

Find the component form and magnitude of the indicated vector.&#10;

Accepted Answer

The component form of $\overrightarrow{\mathrm{PQ}}$ is found by subtracting the coordinates of P from Q, resulting in $\langle 9 - 8, 16 - 9 \rangle = \langle 1, 7 \rangle$. The magnitude is $\sqrt{(1)^2 + (7)^2} = \sqrt{1 + 49} = \sqrt{50}$.

Question 9

Find the component form and magnitude of the indicated vector.&#10;

Accepted Answer

To find the component form of $\overrightarrow{\mathrm{PQ}} + 2\overrightarrow{\mathrm{RS}}$, first find the components of $\overrightarrow{\mathrm{PQ}}$ and $\overrightarrow{\mathrm{RS}}$. For $\overrightarrow{\mathrm{PQ}}$, subtract the coordinates of $P$ from $Q$: $(-3 + 4, 13 - 8) = (1, 5)$. For $\overrightarrow{\mathrm{RS}}$, subtract the coordinates of $R$ from $S$: $(7 - 3, 0 - (-5)) = (4, 5)$. Then, multiply $\overrightarrow{\mathrm{RS}}$ by 2: $2(4, 5) = (8, 10)$. Add this to $\overrightarrow{\mathrm{PQ}}$ to get $(1 + 8, 5 + 10) = (9, 15)$. The magnitude of this vector is $\sqrt{9^2 + 15^2} = \sqrt{81 + 225} = \sqrt{306} = 3\sqrt{34}$.

Question 10

R = (6, 3), S = (7, 5), O = (9, 8), and P = (11, 10)&#10;A) No&#10;B) Yes

Accepted Answer

The answer of R = (6, 3), S = (7,...

Question 11

R = (-1, 3), S = (-10, 5), O = (3, -1), and P = (-6, 1)&#10;A) No&#10;B) Yes

Accepted Answer

The answer of R = (-1, 3), S = (-10,...

Question 12

R = (-4, -2), S = (-11, -11), O = (7, -3), and P = (-8, -12)&#10;A) No&#10;B) Yes

Accepted Answer

The answer of R = (-4, -2), S = (-11,...

Question 13

R = (5, 1), S = (8, 10), O = (0, 0), and P = (3, 10)&#10;A) Yes&#10;B) No

Accepted Answer

The answer of R = (5, 1), S = (8,...

Question 14

R = (-6, 3) , S = (-1, 6), O = (0, 0), and P = (5, 3)&#10;A) No&#10;B) Yes

Accepted Answer

The answer of R = (-6, 3) , S =...

Question 15

R = (-4, -2), S = (-1, 4), O = (0, 0), and P = (3, 2)&#10;A) No&#10;B) Yes

Accepted Answer

The answer of R = (-4, -2), S = (-1,...

Question 16

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 17

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 18

Find the component form and magnitude of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form and magnitude of...

Question 19

Find the component form and magnitude of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form and magnitude of...

Question 20

Find the component form and magnitude of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form and magnitude of...

Question 21

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 22

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 23

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 24

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 25

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 26

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 27

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 28

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 29

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 30

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 31

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 32

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 33

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 34

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 35

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 36

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 37

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 38

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.&#10;

Accepted Answer

The answer of Find the unit vector in the direction...

Question 39

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 40

Find the component form of the indicated vector.&#10;

Accepted Answer

The answer of Find the component form of the indicated...

Question 41

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 42

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 43

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 44

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 45

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 46

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 47

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 48

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 49

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 50

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 51

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 52

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 53

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 54

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 55

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 56

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 57

Find the component form of the vector v.&#10;

Accepted Answer

The answer of Find the component form of the vector...

Question 58

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0&#176;, 360&#176;) rounded&#10;to the nearest tenth.&#10;

Accepted Answer

The answer of Find the magnitude and direction angle for...

Question 59

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 60

Solve the problem.&#10;One rope pulls a barge directly east with a force of 83 N, and another rope pulls the barge directly north with a force of 47 N. Find the magnitude of the resultant force acting on the barge.&#10;A) 95 N&#10;B) 3901 N&#10;C) 36 N&#10;D) 130 N

Accepted Answer

The answer of Solve the problem.&#10;One rope pulls a barge...

Question 61

Find a&#183; b.&#10;

Accepted Answer

The answer of Find a&#183; b.&#10; ...

Question 62

Use the dot product to find&#10;

Accepted Answer

The answer of Use the dot product to find&#10; ...

Question 63

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 64

Use the dot product to find&#10;

Accepted Answer

The answer of Use the dot product to find&#10; ...

Deck 6: Applications of Trigonometry