Question

What is the projection of `(-i + j + k)` onto `( i -2j + 3k)`?

Answer 1

No projection since the vectors are perpendicular.

Explanation:

Let `vecb= <-1,1,1>` and `veca= <1,-2,3>`

The vector projection of `vecb` over `veca` is

`=(veca.vecb)/(||veca||^2)*veca`

The dot product is

`veca.vecb=<-1,1,1> . <1,-2,3> =(-1*1)+(1*-2)+(1*3)`

`=-1-2+3=0`

The vectors `veca` and `vecb` are perpendicular.

So there is no projection posiible.