What is the projection of <-8,3,7 > onto <1,4,-3 >?

1 Answer
ali ergin
Feb 14, 2016

vec c=<17/26,68/26,-51/26>

Explanation:

vec a= <-8,3,7>
vec b= <1,4,-3>
vec c= (vec a*vec b)/(|b|.|b|)*vec b
vec a*vec b=-8*1+3*4-3*7=-8+12-21=-17
|vec b|=sqrt(1^2+4^2(-3)^2)=sqrt 26
vec c=-17/(sqrt 26*sqrt 26)*<1,4,-3>
vec c=-17/26<1,4,-3>
vec c=<17/26*1,17/26*4,-17/26*3>
vec c=<17/26,68/26,-51/26>

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