### Home > PC3 > Chapter 11 > Lesson 11.1.2 > Problem11-34

11-34.

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

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

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