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Q. 1

Found in: Page 897


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Projecting one vector onto another: Show that the formula for the projection of a vector v onto a nonzero vector u is given by projuv = u.v|u|, where u0.

Dot product: u.v = uvcosθ,projuv = vcosθ,Solving above two equations we get,projuv = u.vu.

See the step by step solution

Step by Step Solution

Step 1. Given Information.

Given two vectors u and v where u is a nonzero vector.

Step 2. Dot product.

u.v = u.vcosθ

Step 3. Proof

Let suppose we have a vector v and another vector u and these vectorsmake an angle of θ between them,Now, the we take the component of the v along the u we getcompuv = vcosθ,Now the projection is the same as the component we can write,projuv = compuv = vcosθNow multiply divide by the magnitude of u vector in the numerator and denominator in the RHS, we get,projuv = vucosθu,Now from dot product we get,projuv = u.vu.

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