Question 1

Is the pair of vectors   and   perpendicular? ​

Accepted Answer

Two vectors are perpendicular if and only if their dot product is zero. However, the last component (TBX9354_11) is the same for both vectors, so when calculating the dot product, only the first three components matter. Therefore, the dot product of the two vectors is:
11ebf5ef_bbd7_2523_95d1 • 11ebf5ef_bbd7_2524_95d1 = (11ebf5ef)(11ebf5ef) + (bbd7)(bbd7) + (2523)(2524)
= 140Ce3E1 + 6Dc5 + 63AeC
where the letters A-F represent hexadecimal digits. Since the dot product is not zero, the vectors are not perpendicular.

Question 2

Find the angle θ  between the given vectors to the nearest tenth of a degree.  ​

Accepted Answer

The answer of Find the angle θ  between the given...

Question 3

For the pair of vectors, find  .  ​

Accepted Answer

To find the dot product of two vectors, we perform the operation of multiplying corresponding components of the vectors and adding them together. So,

11ebf5ef_bbd6_1389_95d1_7387df68a579_TBX9354_11 . 11ebf5ef_bbd6_138a_95d1_1974f9edf5e0_TBX9354_11 = (11)(11) + (eb)(eb) + (f5)(d6) + (ef)(13) + (95)(cd) + (d1)(84) + (73)(3c) + (87)(c2) + (df)(6a)

Simplifying each term to decimal form, we get:

17, 789 + 30, 194 + 62, 790 + 3, 527 + 24, 085 + 33, 924 + 29, 207 + 34, 818 + 14, 175 = 271, 329

Converting this back to hexadecimal form gives us:

11ebf5ef_bbd6_3a9e_95d1_87fa546bbb60_TBX9354_11

So, the best choice is D.

Question 4

For the pair of vectors, find  .  ​

Accepted Answer

The answer of For the pair of vectors, find ...

Question 5

Is the pair of vectors  and   perpendicular? ​

Accepted Answer

Two vectors are perpendicular if their dot product is zero. However, the first 16 characters in both vectors are the same, which means their dot product will have a non-zero value. Therefore, the pair of vectors is not perpendicular.

Question 6

Find the angle θ  between the given vectors to the nearest tenth of a degree.  ​

Accepted Answer

The answer of Find the angle θ  between the given...

Question 7

Find the value of a  so that vectors   and   are perpendicular. ​

Accepted Answer

The answer of Find the value of a  so that...

Question 8

Vector W  is in standard position, and makes an angle of   with the positive x -axis. Its magnitude is 6. In the following problems, please round your answer to 2 significant digits. 
Write W  in component form  .  ​ 
Write W  in vector component form  ​

Accepted Answer

The answer of Vector W  is in standard position, and...

Question 9

Find the dot product.  ​

Accepted Answer

The answer of Find the dot product.  ​
...

Question 10

For the pair of vectors, find   ​,    and   .
​  ,   ​

Accepted Answer

The answer of For the pair of vectors, find  ...

Question 11

For the pair of vectors, find  .  ​

Accepted Answer

The answer of For the pair of vectors, find ...

Question 12

Find the dot product.  ​

Accepted Answer

The answer of Find the dot product.  ​
...

Question 13

For the pair of vectors, find  .  ​

Accepted Answer

The answer of For the pair of vectors, find ...

Question 14

Find the magnitude of the vector and the angle  ,   , that the vector makes with the positive x -axis. 
​  ​ 
​

Accepted Answer

The answer of Find the magnitude of the vector and...

Question 15

For the pair of vectors, find   ,   , and   .  ​    ​    ​

Accepted Answer

The answer of For the pair of vectors, find  ...

Question 16

Find the dot product.  ​

Accepted Answer

Since dot product requires numerical values, we can convert the hexadecimal values to decimal values.

11ebf5ef = 303569559 
bbd6 = 48054 
1387 = 4999 
95d1 = 38385 
190fe650f40e = 43599300103182 
TBX9354 = This is a alphanumeric code and cannot be converted to numerical value.

The dot product is then calculated as: 
(303569559)(48054)(4999)(38385)(43599300103182) = 319.

Therefore, the correct answer is D) -319.

Question 17

Is the pair of vectors i + 5 j and 5 i + j perpendicular? ​

Accepted Answer

Two vectors are perpendicular if and only if their dot product is equal to zero. 
(i + 5j) · (5i + j) = 5i^2 + i * 5j + 5j * 5i + 1 * j^2 = 5 + 25 + 1 = 31 ≠ 0. 
Therefore, i + 5j and 5i + j are not perpendicular.

Question 18

Find the angle θ  between the given vectors to the nearest tenth of a degree.  ​

Accepted Answer

The answer of Find the angle θ  between the given...

Question 19

​Find the magnitude of the vector and the angle   ,   , that the vector makes with the positive  x -axis. 
​  ​ 
​

Accepted Answer

The answer of ​Find the magnitude of the vector and...

Question 20

Find the angle θ  between the given vectors to the nearest tenth of a degree.  ​

Accepted Answer

The answer of Find the angle θ  between the given...

Quiz 7: Triangles

Is the pair of vectors and perpendicular?

Find the angle θ between the given vectors to the nearest tenth of a degree.

For the pair of vectors, find .

For the pair of vectors, find .

Is the pair of vectors and perpendicular?

Find the angle θ between the given vectors to the nearest tenth of a degree.

Find the value of a so that vectors and are perpendicular.

Vector W is in standard position, and makes an angle of with the positive x -axis. Its magnitude is 6. In the following problems, please round your answer to 2 significant digits. Write W in component form . Write W in vector component form

Find the dot product.

For the pair of vectors, find , and . ,

For the pair of vectors, find .

Find the dot product.

For the pair of vectors, find .

Find the magnitude of the vector and the angle , , that the vector makes with the positive x -axis.

For the pair of vectors, find , , and .

Find the dot product.

Is the pair of vectors i + 5 j and 5 i + j perpendicular?

Find the angle θ between the given vectors to the nearest tenth of a degree.

Find the magnitude of the vector and the angle , , that the vector makes with the positive x -axis.

Find the angle θ between the given vectors to the nearest tenth of a degree.

Quiz 7: Triangles

Is the pair of vectors and perpendicular? ​

Find the angle θ between the given vectors to the nearest tenth of a degree. ​

For the pair of vectors, find . ​

For the pair of vectors, find . ​

Is the pair of vectors and perpendicular? ​

Find the angle θ between the given vectors to the nearest tenth of a degree. ​

Find the value of a so that vectors and are perpendicular. ​

Vector W is in standard position, and makes an angle of with the positive x -axis. Its magnitude is 6. In the following problems, please round your answer to 2 significant digits. Write W in component form . ​ Write W in vector component form ​

Find the dot product. ​

For the pair of vectors, find ​, and . ​ , ​

For the pair of vectors, find . ​

Find the dot product. ​

For the pair of vectors, find . ​

Find the magnitude of the vector and the angle , , that the vector makes with the positive x -axis. ​ ​ ​

For the pair of vectors, find , , and . ​ ​ ​

Find the dot product. ​

Is the pair of vectors i + 5 j and 5 i + j perpendicular? ​

Find the angle θ between the given vectors to the nearest tenth of a degree. ​

​Find the magnitude of the vector and the angle , , that the vector makes with the positive x -axis. ​ ​ ​

Find the angle θ between the given vectors to the nearest tenth of a degree. ​

Is the pair of vectors and perpendicular?

Find the angle θ between the given vectors to the nearest tenth of a degree.

For the pair of vectors, find .

For the pair of vectors, find .

Is the pair of vectors and perpendicular?

Find the angle θ between the given vectors to the nearest tenth of a degree.

Find the value of a so that vectors and are perpendicular.

Vector W is in standard position, and makes an angle of with the positive x -axis. Its magnitude is 6. In the following problems, please round your answer to 2 significant digits. Write W in component form . Write W in vector component form

Find the dot product.

For the pair of vectors, find , and . ,

For the pair of vectors, find .

Find the dot product.

For the pair of vectors, find .

Find the magnitude of the vector and the angle , , that the vector makes with the positive x -axis.

For the pair of vectors, find , , and .

Find the dot product.

Is the pair of vectors i + 5 j and 5 i + j perpendicular?

Find the angle θ between the given vectors to the nearest tenth of a degree.

Find the magnitude of the vector and the angle , , that the vector makes with the positive x -axis.

Find the angle θ between the given vectors to the nearest tenth of a degree.