Question

given $vec{g}=langle3, - 5
angle$ and $vec{h}=langle - 4,6
angle$, find $4vec{g}+3vec{h}$. a $langle - 4,3
angle$ b $langle0, - 2
angle$ c $langle30, - 32
angle$ d $langle - 12,12
angle$

Explanation:

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

Multiply each component of $\vec{g}=\langle3,- 5
angle$ by 4. So, $4\vec{g}=4\langle3,-5
angle=\langle4\times3,4\times(-5)
angle=\langle12,-20
angle$.

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

Multiply each component of $\vec{h}=\langle - 4,6
angle$ by 3. So, $3\vec{h}=3\langle - 4,6
angle=\langle3\times(-4),3\times6
angle=\langle - 12,18
angle$.

Step3: Add the two resulting vectors

Add the corresponding components of $4\vec{g}$ and $3\vec{h}$. $(4\vec{g}+3\vec{h})=\langle12+( - 12),-20 + 18
angle=\langle0,-2
angle$.

Answer:

B. $\langle0,-2
angle$