What is the projection of $<4 , -6, 7 >$ onto $< -1 , 9,-2 >$ ?

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Answer 1 · 2017-07-22T14:32:20

The vector projection is $=-72/86<-1,9,-2>$
The scalar projection is $=-72/sqrt86$

Let $vecb= <4,-6,7>$ and $veca= <-1,9,-2>$

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

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

The dot product is

$veca.vecb=<4,-6,7> . <-1,9,-2> =(4*-1)+(-6*9)+(7*-2)$

$=-4-54-14=-72$

The modulus of $veca$ is

$||<-1,9,-2>|| =sqrt(1+81+4) = sqrt86$

Therefore,

The vector projection is

$=-72/86<-1,9,-2>$

The scalar projection is

$=(veca.vecb)/(||veca||)=-72/sqrt86$

What is the projection of <4 , -6, 7 ><4 , -6, 7 > onto < -1 , 9,-2 >< -1 , 9,-2 >?