What is the projection of #< 6 , -6 ,3 ># onto #< 4, -5, 1>#?

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Answer 1 · 2016-03-14T19:47:21

=#<228/42, (-285)/42, 57/42>#

Projection of a vector a on another vector b (component of a along b )is given by

#Proj_b a# = #( **a** . **b** )/ ||b||^2 **b** #
Hence if a is <6,-6,3> and b is < 4,-5,1>
a . b = 24 +30 +3 =57

#||b||^2 = 4^2 +(-5)^2 +1^2#=42

Hence,#Proj_b a= 57/42 <4,-5,1>#

=#<228/42, (-285)/42, 57/42>#