What is the projection of $< -2, 4, 7>$ onto $< -5, 9, -5>$ ?

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Answer 1 · 2018-07-22T17:45:32

The projection is $=(11)/131*<-5,9,-5>$

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

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

Here,

$veca= <-5,9,-5>$

$vecb = <-2,4,7>$

Therefore,

The dot product is

$veca.vecb=<-5,9,-5> . <-2,4,7> =10+36-35=11$

The modulus of $veca$ is

$|veca| = |<-5,9,-5>| = sqrt(25+81+25)= sqrt131$

Therefore

$proj_(veca)vecb=(11)/131*<-5,9,-5>$

What is the projection of < -2, 4, 7>< -2, 4, 7> onto < -5, 9, -5>< -5, 9, -5>?