Question

what is the magnitude of \\(vec{v}\\)? \\((8, -2)\\) \\(|vec{v}| = ?\\) round your answer to the nearest hundredth.

Explanation:

Step1: State magnitude formula

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

Step2: Substitute values

$x=8$, $y=-2$, so $|\vec{v}|=\sqrt{8^2+(-2)^2}$

Step3: Calculate squared terms

$8^2=64$, $(-2)^2=4$, so $|\vec{v}|=\sqrt{64+4}$

Step4: Sum and simplify root

$64+4=68$, so $|\vec{v}|=\sqrt{68}$

Step5: Compute decimal & round

$\sqrt{68}\approx8.246$, rounded to 8.25

Answer:

8.25