Question

What is the projection of `(3i + 2j - 6k)` onto `(3i - j - 2k)`?

Answer 1

The answer is `=19/(7sqrt14)(3i-j-2k)`

Explanation:

Let `veca=〈3,-1,-2〉` and `vecb=〈3,2,-6〉`
Then the vector projection of `vecb` upon `veca` is
`(veca.vecb)/(∥veca∥∥vecb∥)veca`
The dot product `veca.vecb=〈3,-1,-2〉.〈3,2,-6〉=9-2+12=19`
The modulus `∥veca∥=sqrt(9+1+4)=sqrt14`
The modulus `∥vecb∥=sqrt(9+4+36)=sqrt49=7`
the projection is `=19/(7sqrt14)〈3,-1,-2〉`