If overrightarrow{A} and overrightarrow{B} ar | vedclass

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Question

(D) The cross product $\overrightarrow{C} = \overrightarrow{A} 	imes \overrightarrow{B}$ is a vector that is perpendicular to both $\overrightarrow{A

Vedclass · Accepted Answer

$(a), (b), (c), (d)$

Vedclass · Answer

(D) The cross product $\overrightarrow{C} = \overrightarrow{A} 	imes \overrightarrow{B}$ is a vector that is perpendicular to both $\overrightarrow{A}$ and $\overrightarrow{B}$.Since $\overrightarrow{A} 	imes \overrightarrow{B}$ is perpendicular to the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$,it must be perpendicular to any vector lying in that plane.Both $(\overrightarrow{A} + \overrightarrow{B})$ and $(\overrightarrow{A} - \overrightarrow{B})$ are linear combinations of $\overrightarrow{A}$ and $\overrightarrow{B}$,meaning they lie in the same plane.Therefore,$(\overrightarrow{A} 	imes \overrightarrow{B}) \perp (\overrightarrow{A} + \overrightarrow{B})$ and $(\overrightarrow{A} 	imes \overrightarrow{B}) \perp (\overrightarrow{A} - \overrightarrow{B})$ are both correct.Statement $(e)$ is incorrect because $\overrightarrow{A} \cdot \overrightarrow{B}$ is a scalar,not a vector,and the concept of perpendicularity is defined for vectors.

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