Question

What is the projection of `<-8,3,7 >` onto `<1,4,-3 >`?

Answer 1

`vec c=<17/26,68/26,-51/26>`

Explanation:

`vec a= <-8,3,7>`
`vec b= <1,4,-3>`
`vec c= (vec a*vec b)/(|b|.|b|)*vec b`
`vec a*vec b=-8*1+3*4-3*7=-8+12-21=-17`
`|vec b|=sqrt(1^2+4^2(-3)^2)=sqrt 26`
`vec c=-17/(sqrt 26*sqrt 26)*<1,4,-3>`
`vec c=-17/26<1,4,-3>`
`vec c=<17/26*1,17/26*4,-17/26*3>`
`vec c=<17/26,68/26,-51/26>`