Dot Products in Physics denote scalar results fmo vector products, e.g Work = F.D = FDCos(FD) a scalar result from the dot product of two vectors, F Force and D Displacement.
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We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.
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Mathematics is the language of physics, and all the sciences are branches of physics. So if we are to explain, describe, or understand anything in our universe, we must use mathematics in one form or another to come to that understanding.
Work is defined as the dot product of force times distance, or W = F * d = Fd cos (theta) where theta is the angle in between the force and distance vectors (if you are doing two dimensions). In three dimensions, use the standard definition for the dot product (using the component form of the vectors).