Question

given that a vector is the directed line segment from p(0,0) to q(3,2), what is the magnitude of that vector? 13 1 √13 √8

Explanation:

Step1: Find the vector components

Subtract $P$ coordinates from $Q$ coordinates:
$\vec{PQ} = (3-0, 2-1) = (3,1)$

Step2: Calculate the magnitude

Use the magnitude formula for $\vec{v}=(x,y)$: $|\vec{v}|=\sqrt{x^2+y^2}$
$|\vec{PQ}| = \sqrt{3^2 + 1^2} = \sqrt{9+1} = \sqrt{13}$

Answer:

$\sqrt{13}$ (Option: $\sqrt{13}$)