Question

HELP! May someone describe projections geometrically!?

Answer 1

Here is a diagram of a scalar projection of one vector onto another. The projection is like the "shadow" where one takes the endpoint of the vector and constructs a perpendicular to the othe vector. The area from the vertex to the perpendicular on the second vector is the projection.

Answer 2

Oh alright, so can I say that"A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines.
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Answer 3

That would be a 3-dimensional definition. It doesn't have to be 3-dimensional, it could be 2-dimensional as in the above diagram. You could however, extend the diagram above by not requiring that the "angled" vector be in the same plane. You could visualize that it belongs to a plane that is perpendicular to the computer screen, like the edge of a cardboard box.

Answer 4

So, your definition would be more general and would accommodate the diagram. You could go with the definition you presented.

Answer 5

Oh so if I were to use your diagram I would say a Projection is: The projection is like the "shadow" where one takes the endpoint of the vector and constructs a perpendicular to the othe vector. The area from the vertex to the perpendicular on the second vector is the projection. The "shadow" should be parallel to the other vector.."

Answer 6

But if I were to explain it my method it would still be ok?

Answer 7

Yes, as long as you are prepared to answer question on it when asked! Someone might ask you about what you mean by parallel lines. Tell them that the transformation or projection of each point travels in the same direction when projecting. I'll draw a picture.Consider all those parallel lines as dotted lines just showing the path for the projection, and also consider that there are infinitely many, just like there are infinitely many points on a line segment.