Question

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

Explanation:

Step1: Multiply vectors by scalars

For vector \(\vec{g}=\langle3,-5
angle\), \(4\vec{g} = 4\langle3,-5
angle=\langle4\times3,4\times(-5)
angle=\langle12,-20
angle\)
For vector \(\vec{h}=\langle - 4,6
angle\), \(3\vec{h}=3\langle - 4,6
angle=\langle3\times(-4),3\times6
angle=\langle - 12,18
angle\)

Step2: Add the two new vectors

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

Answer:

B. \(\langle0,-2
angle\)