THE ARK OF MATHEMATICS PART 3: PROVING VECTORS AND VECTOR PRODUCTS by Chad Clawitter

Author:Chad Clawitter [Clawitter, Chad]
Language: eng
Format: azw3, pdf
Published: 2019-03-27T16:00:00+00:00

We can combine these two properties together to represent the dot product of two vectors as a function of the magnitude of the difference of the vectors and the magnitude of the sum of the vectors.

The dot product between two vectors stays the same when you rotate both vectors by the same angle. The magnitudes of the vectors stay the same for a rotation, and the magnitude of the vector difference and magnitude of the vector difference stay the same if the vectors are rotated by the same angle. Since the dot product is a function of these magnitudes, the dot product also stays the same if both vectors are rotated by the same angle.

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