Question

A vector A has an x component Ax =3 and a y component Ay= -1. What are the x and y components of the vector 2A? The vector -4A?

Answer 1

The vector can be written as:

$$\vec{A} = (3,-1)$$

Then

$$2\vec{A} = 2\cdot (3,-1) = (2\cdot 3,2\cdot(-1)) = (6,-2)$$ $$-4\vec{A} = (-4)\cdot (3,-1) = ((-4)\cdot 3,(-4)\cdot(-1)) = (-12,4)$$

Answer. $2\vec{A} = (6,-2)$ and $-4\vec{A} =(-12,4)$.