Question

A vector A has X components Ax =3 and a Y components Ay= -1. What are the X and Y components of the vector 2A? The vector -4A?

Answer 1

Multiplication of vector is componentwise: $\lambda (x,y) = (\lambda x, \lambda y)$.

Therefore, given that $\bold a = (3, -1)$, vector:

$2 \bold a$ is equal to $(6, -2)$ (has x-component 6 and y-component -2)

$-4 \bold a$ is equal to $(-12, 4)$ (has x-component -12 and y-component 4)