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

1 Answer
ali ergin
Feb 18, 2016

vec c=(-25/21,-50/21,100/21)→c=(−2521,−5021,10021)

Explanation:

vec a=(3,-6,4)→a=(3,−6,4)
vec b=(1,2,-4)→b=(1,2,−4)
vec c=(vec a*vec b)/||b||^2*vec b→c=→a⋅→b||b||2⋅→b
step-1": find dot product of a and b"step−1: find dot product of a and b
vec a*vec b=3.1-2*6-4*4=3-12-16=-25→a⋅→b=3.1−2⋅6−4⋅4=3−12−16=−25
step-2":find magnitude of the vector of b"step−2:find magnitude of the vector of b
||b||^2=1^2+2^2+(-4)^2=1+4+16=21||b||2=12+22+(−4)2=1+4+16=21
step-3:step−3:
vec c=-25/21(1,2,-4)→c=−2521(1,2,−4)
vec c=(-25/21,-50/21,100/21)→c=(−2521,−5021,10021)

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