If overrightarrow{A} times overrightarrow{B} | vedclass

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(D) By the definition of the cross product,the vector $\overrightarrow{C} + \overrightarrow{D}$ is perpendicular to both $\overrightarrow{A}$ and $\ov

Vedclass · Accepted Answer

Component of $\overrightarrow{C}$ along $\overrightarrow{A} = -$ component of $\overrightarrow{D}$ along $\overrightarrow{A}$

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(D) By the definition of the cross product,the vector $\overrightarrow{C} + \overrightarrow{D}$ is perpendicular to both $\overrightarrow{A}$ and $\overrightarrow{B}$.Therefore,the dot product of $\overrightarrow{A}$ with $(\overrightarrow{C} + \overrightarrow{D})$ must be zero:$\overrightarrow{A} \cdot (\overrightarrow{C} + \overrightarrow{D}) = 0$Expanding this,we get:$\overrightarrow{A} \cdot \overrightarrow{C} + \overrightarrow{A} \cdot \overrightarrow{D} = 0$Since the component of a vector $\vec{V}$ along $\vec{A}$ is given by $\frac{\vec{V} \cdot \vec{A}}{|A|}$,we can write:$|A| 	imes (	ext{component of } \overrightarrow{C} 	ext{ along } \overrightarrow{A}) + |A| 	imes (	ext{component of } \overrightarrow{D} 	ext{ along } \overrightarrow{A}) = 0$Dividing by $|A|$ (assuming $\overrightarrow{A} 
eq 0$):Component of $\overrightarrow{C}$ along $\overrightarrow{A} = -$ component of $\overrightarrow{D}$ along $\overrightarrow{A}$.

If $\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C} + \overrightarrow{D},$ then select the correct alternative-

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