Qstnid -A-12-can You Have A→×b→=a→·b→with A ≠ 0 And B ≠ 0? What If One Of The Two Vectors Is Zero? - 02: Physics And Mathematics

with Solutions -

#12
Can you have
A→×B→=A→·B→with A ≠ 0 and B ≠ 0? What if one of the two vectors is zero?
Ans : No, we cannot have `` \stackrel{\to }{A}\times \stackrel{\to }{B}=\stackrel{\to }{A}·\stackrel{\to }{B}`` with A ≠ 0 and B ≠ 0. This is because the left hand side of the given equation gives a vector quantity, while the right hand side gives a scalar quantity. However, if one of the two vectors is zero, then both the sides will be equal to zero and the relation will be valid.
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