What is the projection of < 0 , 2, -2 ><0,2,−2> onto < 3 , -6, 7 ><3,−6,7>?

1 Answer
bp
Jan 1, 2017

Proj_vec v vec u= (-26)/94 <3,-6,7>Proj→v→u=−2694<3,−6,7> =< (-78)/94, 156/94, (-182)/94 ><−7894,15694,−18294>

Explanation:

Let vec u→u be <0,2,-2> and vec v→v be <3,-6,7>. The projection of vec u→u on vec v→v is represented as

Proj_vec v vec uProj→v→u = (vec u .vec v) /||vec v||^2 vec v→u.→v∣∣∣∣→v∣∣∣∣2→v

In the present case vec u .vec v→u.→v = 0(3) +2(-6) +(-2)(7) = -26

Also ||v||^2||v||2 = 3^2 +(-6)^2 + 7^232+(−6)2+72 = 94

Thus Proj_vec v vec u= (-26)/94 <3,-6,7>Proj→v→u=−2694<3,−6,7> =< (-78)/94, 156/94, (-182)/94 ><−7894,15694,−18294>

Related questions
See all questions in Vectors
Impact of this question
1536 views around the world
You can reuse this answer
Creative Commons License