What is the projection of $<6,-4,9 >$ onto $<7,8,7 >$ ?

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Answer 1 · 2017-02-04T07:44:38

The vector projection is $=73/162<7,8,7>$
The scalar projection $=73/sqrt162$

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

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

The dot product is

$veca.vecb=<7,8,7>.<6,-4,9>=42-32+63=73$

The modulus of $veca$ is

$||veca||=||<7,8,7>||=sqrt(49+64+49)=sqrt162$

The vector projection is

$=73/162<7,8,7>$

The scalar projection is

$(veca.vecb)/(||veca||)=73/sqrt162$

What is the projection of <6,-4,9 ><6,-4,9 > onto <7,8,7 ><7,8,7 >?