Question

given $vec{g}=(3, - 5)$ and $vec{h}=(-4,6)$, find $4vec{g}+3vec{h}$. a $(-4,3)$ b $(0, - 2)$ c $(30, - 32)$ d $(-12,12)$

Explanation:

Step1: Multiply vector $\vec{g}$ by 4

$4\vec{g}=4\langle3,- 5
angle=\langle4\times3,4\times(-5)
angle=\langle12,-20
angle$

Step2: Multiply vector $\vec{h}$ by 3

$3\vec{h}=3\langle - 4,6
angle=\langle3\times(-4),3\times6
angle=\langle - 12,18
angle$

Step3: Add the two resulting vectors

$4\vec{g}+3\vec{h}=\langle12+( - 12),-20 + 18
angle=\langle0,-2
angle$

Answer:

B. $\langle0,-2
angle$