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

1 Answer
Feb 14, 2016

Answer:

#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>#