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

Explanation for the correct option:From the definition of vector product , C must be perpendicular to the plane formed by vector A and B. Thus C⊥Aand B. Also ve ...

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Byju's Answer

Standard XIII

Physics

Multiplication with Vectors

If A ×B = C, ...

Question

If $\vec{A} \times \vec{B} = \vec{C}$ , then which of the following is wrong

$\vec{C} ⊥ \vec{A}$

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$\vec{C} ⊥ \vec{B}$

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$\vec{C} ⊥ (\vec{A} + \vec{B})$

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$\vec{C} ⊥ (\vec{A} \times \vec{B})$

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Solution

The correct option is D
$\vec{C} ⊥ (\vec{A} \times \vec{B})$

Explanation for the correct option:
From the definition of vector product , $\vec{C}$ must be perpendicular to the plane formed by vector $\vec{A}$ and $\vec{B}$ .
Thus $\vec{C} ⊥ \vec{A}$ and $\vec{B}$ .
Also vector $(\vec{A} + \vec{B})$ lie in the plane formed by vector $\vec{A}$ and $\vec{B}$ .
Thus $\vec{C} ⊥ (\vec{A} + \vec{B})$ .
Cross product $(\vec{A} \times \vec{B}) = \vec{C}$ which can not be perpendicular to itself.
Hence, Option ‘D’ is Correct.

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

If $\vec{A} \times \vec{B} = \vec{C}$ , then which of the following is wrong