Question

Find the unit vector of -2i-j.

Answer 1

<
`(-2√(5) )/(5)`,
`(-√(5) )/(5)`>

Explanation:

-2i - j = <-2, -1> = v

unit vector = u =
`(v)/(||v||)`

||v|| =
`\sqrt{(-2)^(2)+ (-1)^(2)}` =
`√(4+1)` =
`√(5)`

So the unit vector is
`(<-2,-1>)/(√(5))` = <
`(-2)/(√(5) )`,
`(-1)/(√(5) )`>

When we simplify the square root, this becomes <
`(-2√(5) )/(5)`,
`(-√(5) )/(5)`>.