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The dot product of two vectors vanishes ...

The dot product of two vectors vanishes when vectors are orthogonal and has maximum value when vectors are parallel to each other. Explain.

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We know that ` vec A.vec B =AB cos theta , when vetors are orthogonal, ` theta 90^@ , so, When vectors are parallel, ` theta =0^@ ,
So, vec A. vec B = AB cos 0^@ = AB (max.)`.
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