given that a vector is the directed line segment from $p(0,0)$ to $q(3,2)$, what is the magnitude of that…

given that a vector is the directed line segment from $p(0,0)$ to $q(3,2)$, what is the magnitude of that vector? $sqrt{5}$ $sqrt{13}$ 1 13

given that a vector is the directed line segment from $p(0,0)$ to $q(3,2)$, what is the magnitude of that vector? $sqrt{5}$ $sqrt{13}$ 1 13

Answer

Explanation:

Step1: Identify vector components

If a vector is from $P(0,0)$ to $Q(3,2)$, the components of the vector $\vec{v}$ are $v_x = 3 - 0=3$ and $v_y=2 - 0 = 2$.

Step2: Apply magnitude formula

The magnitude of a two - dimensional vector $\vec{v}=(v_x,v_y)$ is given by $|\vec{v}|=\sqrt{v_x^{2}+v_y^{2}}$. Substitute $v_x = 3$ and $v_y = 2$ into the formula: $|\vec{v}|=\sqrt{3^{2}+2^{2}}=\sqrt{9 + 4}=\sqrt{13}$.

Answer:

$\sqrt{13}$