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Weamp;#39;ve known for several videos now that the dot product of two nonzero vectors, a and b, is equal to the length of vector a times the length of vector b times the cosine of the angle between them. Let me draw a and b just to make it clear. If thatamp;#39;s my vector a and thatamp;#39;s my vector b right there, the angle between them is this angle. And we defined it in this way. And actually, if you ever want to solve-- if you have two vectors and you want to solve for that angle, and Iamp;#39;ve never done this before explicitly. And I thought, well, I might as well do it right now. You could just solve for your theta. So it would be a dot b divided by the lengths of your two vectors multiplied by each other is equal to the cosine of theta. And then to solve for theta you would have to take the inverse cosine of both sides, or the arc cosine of both sides, and you would get theta is equal to arc cosine of a dot b over the magnitudes or the lengths of the products of, or the