What is the projection of $<8,-5,3 >$ onto $<7,6,0 >$ ?

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Answer 1 · 2018-02-05T07:00:23

The projection is $=26/85<7,6,0>$

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

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

$veca= <7,6,0>$

$vecb= <8,-5,3>$

The dot product is

$veca.vecb= <7,6,0> . <8, -5,3> = (7)*(8)+(6)*(-5)+(0)*(3)$

$=56-30+0=26$

The modulus of $veca$ is

$||veca|| = ||<7,6,0>|| = sqrt((7)^2+(6)^2+(0)^2)$

$= sqrt(49+36+0)=sqrt(85)$

Therefore,

$proj_(veca)vecb=(26)/(sqrt85)^2* <7,6,0>$

$=26/85<7,6,0>$

What is the projection of <8,-5,3 ><8,-5,3 > onto <7,6,0 ><7,6,0 >?