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1. The problem statement, all variables and given/known data

10. A vector [itex] \vec{u} [/itex] with direction angles A1, B1, and Y1, is perpendicular to a vector [itex] \vec{v} [/itex] with direction angles A2, B2, and Y2. Prove that:

[itex] \cos A1 \cos B2 + \cos B1 \cos B2 + \cos Y1 \cos Y2 = 0[/itex].

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3. The attempt at a solution

I let [itex] \vec{u} = [a, b, c], \vec{v} = [x, y, z] [/itex].

Since these are perpendicular, therefore:

[itex] \vec{u} \bullet \vec{v} = ax + by + cz = 0 [/itex].

Also, [itex] a, b, c, x, y, z [/itex] would all correspond to their direction cosines.

However, I do not understand how I can prove the above statement with these facts. For example, would [itex] \cos A1 \cos A2 = 0 [/itex] simply because they are the components of two vectors which are parallel to each other?

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# Homework Help: Direction angles - Proof

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