If A - B - C- then which of the following statement is wrong- A- C- A- C - BC- C- A - B D- C-A-B-

The correct option is D C⊥ (A×B)From the definition of vector product, C must be perpendicular to the plane formed by vector A and B. nbsp;Thus C⊥A and B. ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If A × B = C,...

Question

If $\to A \times \to B = \to C,$ then which of the following statement is wrong?

\to C ⊥ \to A

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\to C ⊥ \to B

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\to C ⊥ (\to A + \to B)

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\to C ⊥ (\to A \times \to B)

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Solution

The correct option is D $\to C ⊥ (\to A \times \to B)$
From the definition of vector product, $\to C$ must be perpendicular to the plane formed by vector $\to A$ and $\to B .$ Thus $\to C ⊥ \to A$ and $\to B .$ Also $\to A + \to B$ vector must lie in the plane formed by vector $\to A$ and $\to B .$ Thus $\to C ⊥ (\to A + \to B) .$
Cross product $(\to A \times \to B) = \to C$ which can not be perpendicular to itself.
Hence, option (d) is wrong.

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If →A×→B=→C, then which of the following statement is wrong?

If $\to A \times \to B = \to C,$ then which of the following statement is wrong?