What is the projection of #<4,9,1 ># onto #<-1,7,2 >#?

1 Answer
Apr 7, 2016

Answer:

#61/sqrt54#

Explanation:

#vec A={4,9,1}# and #vec B={-1,7,2}#

Projection of #vec A# on #vec B# is the dot product of #vec A# and unit vector #vec B#.

Hence;
#vec A * hat B#
#=vec A * (vec B)/(|vec B|)#
#={4,9,1}.({-1,7,2})/(sqrt(1^2+7^2+2^2))#
#=(4*(-1)+9*7+1*2)/sqrt54#
#=61/sqrt54#