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Exercise 3.6

Express the projection of v ⟶ on w ⟶ in terms of dot products and the vector w ⟶ .

Solution:

This is a vector in the direction of w ⟶ whose magnitude is that of the component of v ⟶ in that direction. ( v ⟶ , w ⟶ ) ( w ⟶ , w ⟶ ) w ⟶ is a vector with exactly these properties and is therefore it. This is about the simplest possible answer to this question, and is very easy to evaluate, so it is probably worthwhile remembering that this projection is easy to find.

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