What is the projection of $<4,-6,3 >$ onto $<1,5,2 >$ ?

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Answer 1 · 2018-06-04T08:11:13

The vector projection is $=<-2/3,-10/3,-4/3>$

The projection of $vecv$ onto $vecu$ is

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

$vecu = <1, 5, 2>$

$vecv= <4, -6,3>$

The dot product is

$< vecu, vecv > = <1, 5, 2> .<4, -6,3>$

$=(1xx4)+(5xx-6)+(2xx3)$

$=4-30+6$

$=-20$

The magnitude of $vecu$ is

$< vecu, vecu > = ||<1, 5, 2>|| =sqrt(1^2+(5)^2+2^2)$

$=sqrt(1+25+4)$

$=sqrt30$

Therefore, the vector projection is

$proj_(vecu)(vecv)=-20/30<1, 5, 2>$

$= <-2/3,-10/3,-4/3>$

What is the projection of <4,-6,3 ><4,-6,3 > onto <1,5,2 ><1,5,2 >?