What is the projection of $<2,-5,1 >$ onto $<6,-8,3 >$ ?

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Answer 1 · 2016-12-04T09:34:14

The answer is $=55/109〈6,-8,3〉$

The projection of $vecb$ onto $veca$ is

$=(veca.vecb)/(∥veca∥^2)veca$

Here, $vecb=〈2,-5,1〉$ and $veca=〈6,-8,3〉$

The dot product is

$veca.vecb=〈2,-5,1〉.〈6,-8,3〉=(12+40+3)=55$

The modulus of $veca=∥〈6,-8,3〉∥=sqrt(36+64+9)=sqrt109$

The projection is

$=55/109〈6,-8,3〉$

What is the projection of <2,-5,1 ><2,-5,1 > onto <6,-8,3 ><6,-8,3 >?