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Multiplication of vectors - class-XI
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Three vectors satisfy the relation $\displaystyle \overrightarrow { A } .\overrightarrow { B } =0$ and $\displaystyle \overrightarrow { A } .\overrightarrow { C } =0$, then $\displaystyle \overrightarrow { A } $ is parallel to:
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A
$\displaystyle \overrightarrow { B } \times \overrightarrow { C } $
💡 Explanation:
Using : $\vec{A} \times (\vec{B} \times \vec{C}) = \vec{B} (\vec{A} . \vec{C}) - \vec{C} (\vec{A}.\vec{B})$
Given : $\vec{A}.\vec{C} = 0$ and $\vec{A}.\vec{B} = 0$
$\therefore$ $\vec{A} \times (\vec{B} \times \vec{C}) = \vec{B} (0) - \vec{C} ( 0) = 0$
Thus, $\vec{A}$ is parallel to $(\vec{B} \times \vec{C})$.