What is the projection of (i2j+3k) onto (2i+j+2k)?

1 Answer
Jul 8, 2018

The projection is =<1,12,12>

Explanation:

The projection of b onto a is

projab=a.b(a)2a

The vectors are

a=<2,1,1>

and

b=<1,2,3>

The dot product is

a.b=<2,1,1>.<1,2,3>

=(2×1)+(1×(2))+1×3=22+3=3

The magnitude of a is

a=<2,1,1>=22+12+12=6

Therefore,

projab=36<2,1,1>

=<1,12,12>