Question

What is the projection of `<3,-7,4>` onto `<1,4,0 >`?

Answer 1

The projection is `〈-25/17,-100/17,0〉`

Explanation:

Let `vecb=〈3,-7,4〉` and `veca=〈1,4,0〉`

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

`(veca.vecb)/(∥veca∥^2)veca`

The dot product is `veca.vecb`

`=〈3,-7,4〉.〈1,4,0〉=3*1-7*4+0=-25`

The modulus of `veca=∥1,4,0∥=sqrt(1+16)=sqrt17`

So the vector proection is

`=-25/17〈1,4,0〉=〈-25/17,-100/17,0〉`