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Question

If A×B=B×C=C×A then A+B+C is equal to:

A
zero.
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B
sum of magnitudes.
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C
twice of the sum of magnitudes.
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D
unity.
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Solution

The correct option is B zero.
A×B=B×C=C×A
Let, A+B+C=D
Taking cross product at both sides with A.
A×A+B×A+C×A=D×A0A×B+C×A=D×AD×A=0
Similarly, D×B=0 and D×C=0
Hence, D=0

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