What is the projection of $<-7 , -7, 1 >$ onto $< 4, 0, -2 >$ ?

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Answer 1 · 2017-03-02T10:54:07

The vector projection is $=<-6,0,3>$
The scalar projection is $=-3sqrt5$

The vector projection of $vecu$ onto $vecv$ is

$=(vecu.vecv)/(||vecv||^2)vecv$

The dot product is

$vecu.vecv=<-7,-7,1>,<4,0,-2> =-28+0-2=-30$

The modulus of $vecv$ is

$=||vecv||=||vecv||= ||<4,0,-2||$

$=sqrt(16+0+4)=sqrt20$

The vector projection is

$=-30/20<4,0,-2>$

$= <-6,0,3>$

The scalar projection is

$=(vecu.vecv)/(||vecv||)$

$=-30/sqrt20=-15/sqrt5=-3sqrt5$

What is the projection of <-7 , -7, 1 ><-7 , -7, 1 > onto < 4, 0, -2 >< 4, 0, -2 >?