What is the projection of $<7,-8,3 >$ onto $<5,-6,1 >$ ?

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Answer 1 · 2017-02-19T07:17:35

The vector projection is $=43/31<5,-6,1>$
The scalar projection is $=86/sqrt62$

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

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

The dot product is

$veca.vecb=<5,-6,1>*<7,-8,3>$

$=5*7+(-6*-8)+3*1$

$=35+48+3$

$=86$

The modulus of $veca$ is

$||veca||=||<5,-6,1>||$

$=sqrt(25+36+1)$

$=sqrt62$

The vector projection is

$=86/62*<5,-6,1>$

$=43/31<5,-6,1>$

The scalar projection is

$=(veca.vecb)/(||veca||)$

$=86/sqrt62$

What is the projection of <7,-8,3 ><7,-8,3 > onto <5,-6,1 ><5,-6,1 >?