What is the projection of $<4,0,1 >$ onto $<6,-3,7 >$ ?

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Answer 1 · 2016-12-23T14:50:13

The answer is $=31/94〈6,-3,7〉$

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

$=(veca.vecb)/(∥veca∥)^2veca$

The dot product is $=veca.vecb$
$=〈4,0,1〉.〈6,-3,7〉=(24+0+7)=31$

The modulus of $veca$ is $=∥veca∥=∥〈6,-3,7〉∥$

$=sqrt(36+9+49)= sqrt94$

The vector projection is $=31/94〈6,-3,7〉$

What is the projection of <4,0,1 ><4,0,1 > onto <6,-3,7 ><6,-3,7 >?