Projection of vector a onto vector b?

Linear spaces and subspaces, linear transformations, bases, etc.
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Projection of vector a onto vector b?

Postby mitnord » Tue Feb 24, 2009 1:34 am


I have to vectors:
Vector a is given as (1, 3)
Vector b is given as (7, 2)

How to find the projection of the vector a onto the vector b?


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Postby stapel_eliz » Tue Feb 24, 2009 1:57 pm

Hmm... Your book and / or your instructor were supposed to have covered this material before assigning homework on it.... :roll:

The "projection" of a onto b is defined as the vector c that is orthogonal (perpendicular) to b and satisfies |b|2 + |c|2 = |a|2.

Since b and c are orthogonal, what can you say about their dot product? What can you do with the magnitudes?

For explanations and the formulas to use, try reviewing a few online lessons, such as:

. . . . .Projection of One Vector Onto Another (lesson)
. . . . .MathWorld: Projection (article)
. . . . .Dot Products and Projections (lesson)
. . . . .The projection of a vector
. . . . .Wikipedia: Vector projection
. . . . .How to Project One Vector onto Another
. . . . .Vectors (tutorial)

Once you have learned the basic terms and techniques, please attempt the exercise. If you get stuck, you will then be able to reply with a clear listing of your steps and reasoning so far.

Thank you! :D

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