Question

What is the projection of `(-9 i + j + 2 k)` onto `(14i - 7j - 7k)`?

Answer 1

`proj_vec B vec A = <-7i+3,5j+3,5k>`

Explanation:

`vec A= <-9i+j+2k>`
`vec B= <14i-7j-7k>`
`proj_vec B vec A =(vec A * vec B)/|| vec B||^2 * vec B`
`vec A * vec B= -9*14 -1*7 -2*7`
`vec A * vec B= -126-7-14=-147`
`|| vec B||^2=14^2+(-7)^2+(-7)^2=196+49+49=294`
`proj_vec B vec A =-147/294 * <14i-7j-7k >`
`proj_vec B vec A = <-7i+3,5j+3,5k>`