CPM Homework Help : PC3 Problem 11-34

Given vectors $\vec { u }= ⟨−3, 2⟩$ , $\vec { v }= ⟨4, 1⟩$ , and $\vec { w } = 2\vec { u } - \vec { v }$ , calculate $\| \vec { w } \|$ and arg( $\vec { w }$ ).

Step:

$\vec{\text{w}} = 2\left\langle -3,2 \right\rangle -\left\langle 4,1 \right\rangle$

Hint:

Sketch the vector. Then use the Pythagorean theorem to calculate length, or $\left|\right|w\left|\right|$ , and inverse tangent to calculate the angle.