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?\n13\n$sqrt{13}$\n$sqrt{5}$\n1

given that a vector is the directed line segment from $p(0,0)$ to $q(3,2)$, what is the magnitude of that vector?\n13\n$sqrt{13}$\n$sqrt{5}$\n1

Answer

Explanation:

Step1: Find the vector components

If a vector has initial - point $P(x_1,y_1)=(0,0)$ and terminal - point $Q(x_2,y_2)=(3,2)$, the vector $\vec{v}=\langle x_2 - x_1,y_2 - y_1\rangle=\langle3 - 0,2 - 0\rangle=\langle3,2\rangle$.

Step2: Use the magnitude formula

The magnitude of a two - dimensional vector $\vec{v}=\langle a,b\rangle$ is given by $|\vec{v}|=\sqrt{a^{2}+b^{2}}$. Here, $a = 3$ and $b = 2$, so $|\vec{v}|=\sqrt{3^{2}+2^{2}}=\sqrt{9 + 4}=\sqrt{13}$.

Answer:

$\sqrt{13}$