Question

What is the projection of `<3,-6,4>` onto `<1,2,-4>`?

Answer 1

`vec c=(-25/21,-50/21,100/21)`

Explanation:

`vec a=(3,-6,4)`
`vec b=(1,2,-4)`
`vec c=(vec a*vec b)/||b||^2*vec b`
`step-1": find dot product of a and b"`
`vec a*vec b=3.1-2*6-4*4=3-12-16=-25`
`step-2":find magnitude of the vector of b"`
`||b||^2=1^2+2^2+(-4)^2=1+4+16=21`
`step-3:`
`vec c=-25/21(1,2,-4)`
`vec c=(-25/21,-50/21,100/21)`