If A-B - B-C - C-A then A - B - C is equal to-

The correct option is B zero. A⃗×B⃗ = B⃗×C⃗ = C⃗×A⃗ Let, A⃗ + B⃗ + C⃗ = D⃗ Taking cross product at both sides with A⃗ . A⃗×A⃗ + B⃗×A⃗ + C⃗×A⃗ ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If A×B = B×...

Question

If $\to A \times \to B = \to B \times \to C = \to C \times \to A$ then $\to A + \to B + \to C$ is equal to:

zero.

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sum of magnitudes.

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twice of the sum of magnitudes.

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unity.

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Solution

The correct option is B zero.
$\to A \times \to B = \to B \times \to C = \to C \times \to A$
Let, $\to A + \to B + \to C = \to D$
Taking cross product at both sides with $\to A$ .
$\to A \times \to A + \to B \times \to A + \to C \times \to A = \to D \times \to A \Rightarrow 0 - \to A \times \to B + \to C \times \to A = \to D \times \to A \Rightarrow \to D \times \to A = 0$
Similarly, $\to D \times \to B = 0$ and $\to D \times \to C = 0$
Hence, $\to D = 0$

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

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