What is the projection of $<2,-7,1 >$ onto $<4,-5,9 >$ ?

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Answer 1 · 2018-04-22T12:01:10

The projection is $=7/sqrt122<4, -5, 9>$

The projection of $vecv$ onto $vecu$ is

$proj_(vecu)(vecv)= (< vecu, vecv >)/ (< vecu, vecu >) vecu$

$vecu = <4, -5, 9>$

$vecv= <2, -7,1>$

The dot product is

$< vecu, vecv > = <4, -5, 9> .<2, -7,1>$

$=(4xx2)+(-5xx2)+(9xx1)$

$=8-10+9$

$=7$

The magnitude of $vecu$ is

$< vecu, vecu > = ||<4, -5, 9>|| =sqrt(4^2+(-5)^2+9^2)$

$=sqrt(16+25+81)$

$=sqrt122$

Therefore,

$proj_(vecu)(vecv)=7/sqrt122<4, -5, 9>$

What is the projection of <2,-7,1 ><2,-7,1 > onto <4,-5,9 ><4,-5,9 >?