Dot product of vector and its unit vector is
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Since the projection of a vector on to itself leaves its magnitude unchanged, the dot product of any vector with itself is the square of that vector's magnitude. Applying this corollary to the unit vectors means that the dot product of any unit vector with itself is one.
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Explanation:
Since the projection of a vector on to itself leaves its magnitude unchanged, the dot product of any vector with itself is the square of that vector's magnitude. Applying this corollary to the unit vectors means that the dot product of any unit vector with itself is one.
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