Question

The initial point of a⃗ is (−2,4), and its terminal point is (−5,−2). What is the value of ‖a⃗ ‖? Give your answer as a simplified radical.

Answer 1

Answer:

$3\sqrt{5}.$

Step-by-step explanation:

It is given that the initial point of $\vec{a}$ is (-2,4) and terminal point is (-5,-2). So, $\vec{a}$ is defined as

$\vec{a}=(-5-(-2))\hat{i}+(-2-4)\hat{j}$

$\vec{a}=(-5+2)\hat{i}+(-2-4)\hat{j}$  

$\vec{a}=-3\hat{i}-6\hat{j}$

The magnitude of $\vec{v}=a\hat{i}+b\hat{j}$ is

$|\vec{v}|=\sqrt{a^2+b^2}$

The magnitude of $\vec{a}$ is

$|\vec{a}|=\sqrt{(-3)^2+(-6)^2}$

$|\vec{a}|=\sqrt{9+36}$

$|\vec{a}|=\sqrt{45}$

$|\vec{a}|=3\sqrt{5}$

Modulus of magnitude is

$||\vec{a}||=|3\sqrt{5}|=3\sqrt{5}$

So, the magnitude of $\vec{a}$ is $3\sqrt{5}.$