What is the projection of # (-9 i + j + 2 k)# onto #(14i - 7j - 7k)#?

1 Answer
Feb 15, 2016

Answer:

#proj_vec B vec A = <-7i+3,5j+3,5k>#

Explanation:

#vec A= <-9i+j+2k>#
#vec B= <14i-7j-7k>#
#proj_vec B vec A =(vec A * vec B)/|| vec B||^2 * vec B #
#vec A * vec B= -9*14 -1*7 -2*7#
#vec A * vec B= -126-7-14=-147#
#|| vec B||^2=14^2+(-7)^2+(-7)^2=196+49+49=294#
#proj_vec B vec A =-147/294 * <14i-7j-7k >#
#proj_vec B vec A = <-7i+3,5j+3,5k>#