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anonymous
 4 years ago
Show that the vector (orthogonal b onto a) = (b  (projection of b onto a)) is orthogonal to a. It is called an orthogonal projection of b.
from chapter Vectors and the Geometry of Space.
Thanks.
anonymous
 4 years ago
Show that the vector (orthogonal b onto a) = (b  (projection of b onto a)) is orthogonal to a. It is called an orthogonal projection of b. from chapter Vectors and the Geometry of Space. Thanks.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Let & be the angle between B und A. We have to show that B  Bcos & A/A is normal to A. Using the dot product we must have (B  Bcos & A/A )·A =0. Since the dot product is distributive with respect to addition, we can write it as: B·A  Bcos & A/A·A = B Acos &  (Bcos & A/A)A^2 = 0, since (Bcos & A/A)A^2 = B Acos &.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.015 minutes ago I posted a reply. I do not understand why the proof is not right. However, I will try to clear some doubts. A/A is the unit vector in the direction of A. A·A = A A cos 0 = A^2, then (Bcos&/A)A·A = BA cos&.
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