What is the projection of #(3i + 2j - 3k)# onto # ( i - j + k)#?

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Answer 1 · 2017-01-31T06:12:59

#< -2/3, 2/3, -2/3 >#

The projection of vector a onto b is...
#( a*b )/| b |^2*b#

In this case, a is < 3, 2,-3 > and b is < 1, -1, 1 >. Plug in these vectors and simplify...

#(< 3, 2,-3 > * < 1, -1, 1 >)/|< 1, -1, 1 >|^2*b#

#(3*1+2*(-1)+(-3)*1)/((sqrt(1^2+(-1)^2+1^2))^2)*b#

#(3-2-3)/sqrt(3)^2*< 1, -1, 1 >#

#-2/3*< 1, -1, 1 >#

#< -2/3, 2/3, -2/3 >#