Question

given $vec{g}=langle3, - 5
angle$ and $vec{h}=langle - 2,3
angle$, find $2vec{g}-2vec{h}$. a $langle10, - 16
angle$ b $langle - 2,1
angle$ c $langle2, - 4
angle$ d $langle1, - 2
angle$

Explanation:

Step1: Calculate 2\(\vec{g}\)

Multiply each component of \(\vec{g}=\langle3, - 5
angle\) by 2. So \(2\vec{g}=2\langle3,-5
angle=\langle2\times3,2\times(- 5)
angle=\langle6,-10
angle\)

Step2: Calculate 2\(\vec{h}\)

Multiply each component of \(\vec{h}=\langle - 2,3
angle\) by 2. So \(2\vec{h}=2\langle - 2,3
angle=\langle2\times(-2),2\times3
angle=\langle - 4,6
angle\)

Step3: Calculate \(2\vec{g}-2\vec{h}\)

Subtract the corresponding components of \(2\vec{h}\) from \(2\vec{g}\). \(\langle6-(-4),-10 - 6
angle=\langle6 + 4,-16
angle=\langle10,-16
angle\)

Answer:

A. \(\langle10,-16
angle\)