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: Calculate \(4\vec{g}\)

Multiply each component of \(\vec{g}=(3,-5)\) by \(4\).
\(4\vec{g}=4\times(3,-5)=(4\times3,4\times(-5))=(12,-20)\)

Step2: Calculate \(3\vec{h}\)

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

Step3: Calculate \(4\vec{g}+3\vec{h}\)

Add the corresponding components of \(4\vec{g}=(12,-20)\) and \(3\vec{h}=(-12,18)\).
\(4\vec{g}+3\vec{h}=(12 + (-12),-20 + 18)=(0,-2)\)

Answer:

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