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(C) Let $\overrightarrow{A}$ and $\overrightarrow{B}$ be two vectors in a plane. The sum $\overrightarrow{A} + \overrightarrow{B}$ is a vector that li

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$\frac{\pi}{2} 	ext{ rad}$

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(C) Let $\overrightarrow{A}$ and $\overrightarrow{B}$ be two vectors in a plane. The sum $\overrightarrow{A} + \overrightarrow{B}$ is a vector that lies in the same plane as $\overrightarrow{A}$ and $\overrightarrow{B}$.By the definition of the cross product,$\overrightarrow{A} 	imes \overrightarrow{B}$ is a vector that is perpendicular to the plane containing both $\overrightarrow{A}$ and $\overrightarrow{B}$.Since the vector $(\overrightarrow{A} + \overrightarrow{B})$ lies in the plane and the vector $(\overrightarrow{A} 	imes \overrightarrow{B})$ is perpendicular to the plane,the angle between them is $90^{\circ}$ or $\frac{\pi}{2} 	ext{ rad}$.Mathematically,the dot product of these two vectors is:$(\overrightarrow{A} + \overrightarrow{B}) \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = \overrightarrow{A} \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) + \overrightarrow{B} \cdot (\overrightarrow{A} 	imes \overrightarrow{B})$Using the property of the scalar triple product,$\overrightarrow{A} \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = 0$ and $\overrightarrow{B} \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = 0$.Therefore,$(\overrightarrow{A} + \overrightarrow{B}) \cdot (\overrightarrow{A} 	imes \overrightarrow{B}) = 0$,which confirms that the vectors are orthogonal,and the angle between them is $90^{\circ}$.

What is the angle between the resultant of $\overrightarrow{A} + \overrightarrow{B}$ and $\overrightarrow{A} \times \overrightarrow{B}$?

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