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.!