Let v = (1,-3) and w = (-2,6). Which of the following is true?

A. The x-component of v is - 2.

B. v*w = 36

C. The y-component of w is 6.

D. w = - 2v

Answer: both option C. The y-component of w is 6 and D. w = - 2v are true.

May be to made a typo when wrote the question and the answer choices.

Justification:

v = (1,-3) and w = (-2,6) area vectors, given by their x, y components.

A. is false, because the x-component of the vector is the first number inside the parenthesis, so the x-component of v is 1.

B. is false. Assuming you mean the dot product of v and w, this is v. w, which is the scalar product, the result is:

v. w = (1) (-2) + (-3) (6) = - 2 - 18 = - 20

C. is true. The y-component of w is the second number inside the parenthesis (-2,6) so y-component of w is 6.

D. is true. - 2v is equal to - 2 (1,-3) = (-2,6) which is equal to w.