Question

Let V = (8, -4) and W = (-4,2).

Which of the following is true?
Check all that apply. (30 pts)

A. V x W = 40
B. The y-component of W is 2.
C. V = -2W
D. The x-component of V is 4.

Answer 1

Option B and C are correct.

Explanation:

Given the vectors V = (8, -4) and W = (-4,2)

we have to check the following options.

Option A: V x W = 40

`A* B=\begin{vmatrix}i&j&k\\8&-4&0\\-4&2&0\end{vmatrix}=0i+0j+k(16-16)=0i+0j+0k`

Hence, not true

Option B: The y-component of W is 2

W = (-4,2)

x-component is -4

y-component is 2

Hence, true

Option C: V = -2W

W=(-4, 2)

V=-2(-4,2)=(8,-4)

which is true

Option D: The x-component of V is 4

V = (8,-4)

x-component is 8

y-component is -4

which is not true.

hence, the option B and C are correct.

Answer 2

The second value in a set of parenthesis is the y value, so B is true.

If you multiplied each value of W by -2, you would get the values for V, so C is also true.

The answer is B and C.