What is the projection of $<-2,2,5 >$ onto $<1,6,9 >$ ?

Question

1384 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-19T10:33:58

The answer is $=55/118〈1,6,9〉$

The projection of $vecb$ onto $veca$ is

$=(veca.vecb)/(∥veca∥^2)veca$

The dot product is $=〈-2,2,5〉.〈1,6,9〉$

$=(-2+12+45)$

$=55$

The modulus of $veca$

$=∥〈1,6,9〉∥$

$=sqrt(1+36+81)=sqrt118$

Therefore,

the projection is

$=55/118〈1,6,9〉$

What is the projection of <-2,2,5 ><-2,2,5 > onto <1,6,9 ><1,6,9 >?