Question

what is the magnitude of \\(vec{w}\\)?\\((-8, 3)\\)\\(vec{w}\\)\\(|vec{w}| = ?\\)round your answer to the nearest hundredth.

Explanation:

Step1: Recall magnitude formula

For vector $\vec{w}=(x,y)$, $|\vec{w}|=\sqrt{x^2+y^2}$

Step2: Substitute $x=-8,y=3$

$|\vec{w}|=\sqrt{(-8)^2+3^2}$

Step3: Calculate inside the square root

$(-8)^2+3^2=64+9=73$

Step4: Compute square root, round to hundredth

$|\vec{w}|=\sqrt{73}\approx8.54$

Answer:

8.54