What is the projection of # <3,-6,4># onto #<1,2,-4>#?

1 Answer
Feb 18, 2016

Answer:

#vec c=(-25/21,-50/21,100/21)#

Explanation:

#vec a=(3,-6,4)#
#vec b=(1,2,-4)#
#vec c=(vec a*vec b)/||b||^2*vec b#
#step-1": find dot product of a and b"#
#vec a*vec b=3.1-2*6-4*4=3-12-16=-25#
#step-2":find magnitude of the vector of b"#
#||b||^2=1^2+2^2+(-4)^2=1+4+16=21#
#step-3:#
#vec c=-25/21(1,2,-4)#
#vec c=(-25/21,-50/21,100/21)#