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

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Answer 1 · 2016-09-18T06:26:08

$Proj_(vecy) vecx =(3/2,-3,7/2)$ .

The Projection Vector of $vecxnevec0$ onto $vecynevec0$ is

denoted by, $Proj_(vecy) vecx$ , and, is defined by,

$Proj_(vecy) vecx ={(vecx*vecy)/||y||^2}vecy$ , where,

$vecx"cancel(bot) vecy$ .

Here, $vecx=(5,-3,2) and vecy=(3,-6,7)$ .

$:. vecx*vecy=5*3+(-3)(-6)+2*7=47$ , and,

$||vecy||^2=9+36+49=94$ .

Hence,

$Proj_(vecy) vecx =47/94(3,-6,7)=1/2(3,-6,7)$ . Thus,

$Proj_(vecy) vecx =(3/2,-3,7/2)$ .

Enjoy Maths.!

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