Question

Find the projection of v on to w if v = ⟨-5,-2⟩ and w = ⟨1,-1⟩

Answer 1

Explanation:

`(\vec v \bullet \vec w)/(||\vec w||)\bullet \vec w`

`\vec v \bullet \vec w = <-5, -2>\bullet <1,-1>= -5+2 = -3`

`||\vec w ||=√(2)`

Hence, the result will be

`(-3√(2) )/(2) <1,-1>`

you can put the scalar in to get

`<-(3√(2 ))/(2) , (3√(2) )/(2) >`