Q95 / 180 · NEET 2013 (Karnataka) · Physics

Vectors $\vec{A}, \vec{B}$, and $\vec{C}$ are such $\vec{A} \cdot \vec{B}=0$ $\vec{A} \cdot \vec{C}=0$. Then the vector parallel is $\vec{A}$ is:

  • A
    $\vec{A} \times \vec{B}$
  • B
    $\vec{B} \times \vec{C}$
  • Correct answer
    C
    $\vec{B} \times \vec{C}$
  • D
    $\vec{B}$ and $\vec{C}$

Solution

From vector produce $$ \vec{A} \times(\vec{B} \times \vec{C})=(\vec{B} \cdot \vec{C}) \vec{B}-(\vec{A} \cdot \vec{B}) \vec{C} $$ Given that $\vec{A} \cdot \vec{B}=0, \vec{A} \cdot \vec{C}=\mathrm{C}$ then $\vec{A} \times(\vec{B} \times \vec{C})=0$ thus vector $A$ is paralles to $\vec{B} \times \vec{C}$

Hence, the correct answer is option: 'C'.

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