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

Question

6259 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-08T08:58:21

The projection is $=<1,1/2,1/2>$

The projection of $vecb$ onto $veca$ is

$proj_(veca)vecb=(veca.vecb)/(||veca||)^2veca$

The vectors are

$veca= <2,1,1 >$

and

$vecb= <1,-2,3>$

The dot product is

$veca.vecb= <2,1,1 > . <1,-2,3>$

$= (2xx1)+(1xx(-2))+ 1xx3=2-2+3=3$

The magnitude of $veca$ is

$||veca|| = <2,1,1> = sqrt(2^2+1^2+1^2)=sqrt6$

Therefore,

$proj_(veca)vecb=(3)/(6)*<2,1,1 >$

$= <1,1/2,1/2>$

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