What is the projection of (i+j+k) onto (3i+2j3k)?

1 Answer
May 8, 2018

The projection is =23i49j+23k

Explanation:

The vector projection of b onto a is

projab=a.b(a)2a

Here

a=<3,2,3>

b=<1,1,1>

The dot product is

a.b=<3,2,3>.<1,1,1>=3+23=4

The maghitude of a is

a=|<3,2,3>|=9+4+9=18

Therefore,

projab=418<3,2,3>

=29<3,2,3>

=<23,49,23>

=23i49j+23k