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(D) The cross product $\overrightarrow C = \overrightarrow A 	imes \overrightarrow B$ results in a vector $\overrightarrow C$ that is perpendicular t

Vedclass · Accepted Answer

$\overrightarrow C \perp (\overrightarrow A 	imes \overrightarrow B)$

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(D) The cross product $\overrightarrow C = \overrightarrow A 	imes \overrightarrow B$ results in a vector $\overrightarrow C$ that is perpendicular to the plane containing both $\overrightarrow A$ and $\overrightarrow B$.Since $\overrightarrow C$ is perpendicular to the plane,it is perpendicular to any vector lying within that plane.$1$. $\overrightarrow C \perp \overrightarrow A$ and $\overrightarrow C \perp \overrightarrow B$ are true by the definition of the cross product.$2$. The vector sum $(\overrightarrow A + \overrightarrow B)$ also lies in the same plane as $\overrightarrow A$ and $\overrightarrow B$,so $\overrightarrow C \perp (\overrightarrow A + \overrightarrow B)$ is also true.$3$. The statement $\overrightarrow C \perp (\overrightarrow A 	imes \overrightarrow B)$ implies $\overrightarrow C \perp \overrightarrow C$,which is impossible for a non-zero vector as a vector cannot be perpendicular to itself. Therefore,this statement is wrong.

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

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