What is the projection of $<6,0,3 >$ onto $<2,5,-7 >$ ?

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Answer 1 · 2016-10-21T20:09:09

The vector projection is $〈-9/39,-45/78,63/78〉$

Let $vecb=〈6,0,3〉$

and $veca=〈2,5,-7〉$

The dot product is $veca.vecb=(6*2+5*0+3*-7)=12-21=-9$

$∣veca∣^2= (4+25+49)=78$

So the projection is
$(veca.vecb)veca / (∣veca∣^2)=-9/78 〈2,5,-7〉$

What is the projection of <6,0,3 ><6,0,3 > onto <2,5,-7 ><2,5,-7 >?