What is the projection of $<3 ,-4, 7 >$ onto $< -1 , 9,-2 >$ ?

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Answer 1 · 2016-12-22T09:28:19

The answer is $=-53/86〈-1,9,-2〉$

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

$=(veca-vecb)/(∣veca∣^2)*veca$

The dot product is

$veca.vecb=〈3,-4,7〉.〈-1,9,-2〉=(-3-36-14)=-53$

The modulus of $veca$ is $=∣〈-1,9,-2〉∣=sqrt(1+81+4)=sqrt86$

The vector projection is

$=-53/86〈-1,9,-2〉$

What is the projection of <3 ,-4, 7 ><3 ,-4, 7 > onto < -1 , 9,-2 >< -1 , 9,-2 >?