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

`3√(5).`

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}|=√(a^2+b^2)`

The magnitude of
`\vec{a}` is

`|\vec{a}|=√((-3)^2+(-6)^2)`

`|\vec{a}|=√(9+36)`

`|\vec{a}|=√(45)`

`|\vec{a}|=3√(5)`

Modulus of magnitude is

`||\vec{a}||=|3√(5)|=3√(5)`

So, the magnitude of
`\vec{a}` is
`3√(5).`