### Home > PC3 > Chapter 9 > Lesson 9.1.2 > Problem9-42

9-42.

Let $\vec { \text{t} }= ⟨−7, −5⟩$, $\vec { \text{u} }= ⟨3, 6⟩$ , and $\vec { \text{v} }= ⟨−2, 3⟩$.

1. What is $\vec { \text{w} }$ if $\vec { \text{w} } = 5\vec { \text{t} }-\vec { \text{u} }+4\vec { \text{v} }$.

$\vec { \text{w} }= 5⟨−7, −5⟩-⟨3, 6⟩ +4⟨-2, 3⟩$

2. What are the magnitude and direction of $\vec { \text{w} }$?

Sketch vector $\text{w}$. Use the Pythagorean Theorem to determine the magnitude.
Use inverse tangent to determine the direction, paying attention to the quadrant when deciding on your answer.