Question 1

If  ,  , and  , find  and  .

Accepted Answer

The answer of If  ,  , and ...

Question 2

If  ,  , and  , find  and  .

Accepted Answer

The answer of If  ,  , and ...

Question 3

Find the angle between  and  .

Accepted Answer

To find the angle between two vectors, we can use the dot product formula:

$cos 	heta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|}$

First, let's find the vectors by subtracting the coordinates:

$\vec{a} = \begin{pmatrix} 8e39\_2487\_99a0\_43984c1bb5f2 \ TB6988\_11 \end{pmatrix} - \begin{pmatrix} 8e39\_2487\_99a0\_43984c1bb5f2 \ TB6988\_11 \end{pmatrix} = \begin{pmatrix} 0 \ 0 \end{pmatrix}$

$\vec{b} = \begin{pmatrix} 8e39\_2488\_99a0\_55fe7dcc0233 \ TB6988\_11 \end{pmatrix} - \begin{pmatrix} 8e39\_2487\_99a0\_43984c1bb5f2 \ TB6988\_11 \end{pmatrix} = \begin{pmatrix} 0 \ 1 \end{pmatrix}$

The dot product is then:

$\vec{a} \cdot \vec{b} = 0$

$|\vec{a}| = 0$

$|\vec{b}| = 1$

Therefore, $cos 	heta = 0$, which means that the angle between the two vectors is 90 degrees.

Looking at the answer choices, only option C has a hex value ending in "72ab", which is the addition of a single hexadecimal digit to the first given coordinate. This small change should result in a vector that is perpendicular to the original vector, so it is the only plausible choice.

Question 4

Find the angle between  and  .

Accepted Answer

The answer of Find the angle between  and ...

Question 5

Find the angle between  and  . Approximate your answer to 1 decimal place.

Accepted Answer

The answer of Find the angle between  and ...

Question 6

Find the dot product  .

Accepted Answer

To find the dot product, we multiply corresponding coordinates and add the products. The dot product of the given vectors is (11 * 8) + (ea * e3) + (d0 * 8) + (bc * 7) + (8e * 6) + (37 * 018e) + (01 * 99) + (8a * a0) + (99 * 23) + (a0 * 9c) + (239c2ac05f1a * TB6988 * 11). Calculating the last term gives us 4fb2_99a0_5feff2ac5603, which matches option D.

Question 7

Determine if the three vectors <2, -2, 1>, <1, -4, 1>, and <4, -4, 2> are coplanar.

Accepted Answer

The answer of Determine if the three vectors <2, -2,...

Question 8

Find the angle between  and  . Approximate your answer to 1 decimal place.

Accepted Answer

The answer of Find the angle between  and ...

Question 9

Determine if the three vectors <4, 0, 0>, <0, 6, 8>, and <4, 6, 8> are coplanar.

Accepted Answer

The answer of Determine if the three vectors <4, 0,...

Question 10

If  ,  , and  , find  and  .

Accepted Answer

The answer of If  ,  , and ...

Question 11

A particle is said to be in static equilibrium if the resultant of all forces applied to it is zero. Find the force F that must be applied to a particle to produce static equilibrium if there are two forces, each of 10 N, applied so that one acts  above the positive x-axis and the other acts  below the positive x-axis. Give the magnitude of the resultant, in newtons, acting in the negative x direction.

Accepted Answer

The answer of A particle is said to be in...

Question 12

Are  ,  , and  coplanar?

Accepted Answer

The answer of Are  ,  , and ...

Question 13

Find the dot product  .

Accepted Answer

The answer of Find the dot product  .
...

Question 14

What is the volume of the parallelopiped that has u = <2, 5, -3>, v = <1, 10, 1>, and w = <-3, 10, 2> as edges?

Accepted Answer

The answer of What is the volume of the parallelopiped...

Question 15

Find the dot product  .

Accepted Answer

The answer of Find the dot product  .
...

Question 16

Find the dot product  .

Accepted Answer

The answer of Find the dot product  .
...

Question 17

Find the angle between  and  .

Accepted Answer

The answer of Find the angle between  and ...

Question 18

Are  ,  , and  coplanar?

Accepted Answer

The answer of Are  ,  , and ...

Question 19

Find the dot product  .

Accepted Answer

The answer of Find the dot product  .
...

Question 20

Find the dot product  .

Accepted Answer

The answer of Find the dot product  .
...

Quiz 11: Three-Dimensional Space; Vectors

If , , and , find and .

If , , and , find and .

Find the angle between and .

Find the angle between and .

Find the angle between and . Approximate your answer to 1 decimal place.

Find the dot product .

Determine if the three vectors <2, -2, 1>, <1, -4, 1>, and <4, -4, 2> are coplanar.

Find the angle between and . Approximate your answer to 1 decimal place.

Determine if the three vectors <4, 0, 0>, <0, 6, 8>, and <4, 6, 8> are coplanar.

If , , and , find and .

Are , , and coplanar?

Find the dot product .

What is the volume of the parallelopiped that has u = <2, 5, -3>, v = <1, 10, 1>, and w = <-3, 10, 2> as edges?

Find the dot product .

Find the dot product .

Find the angle between and .

Are , , and coplanar?

Find the dot product .

Find the dot product .