Statement $(A)$ : If $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{c}$,then $\vec{a} \times (\vec{b} \times \vec{c}) = 0$.
Reason $(R)$ : If $\vec{b}$ is perpendicular to $\vec{c}$,then $\vec{b} \times \vec{c} = 0$.

  • A
    Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.
  • B
    Both $(A)$ and $(R)$ are true and $(R)$ is not the correct explanation of $(A)$.
  • C
    $(A)$ is true but $(R)$ is false.
  • D
    $(A)$ is false but $(R)$ is true.

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Let $\overline{a}=\hat{j}-\hat{k}$ and $\overline{c}=\hat{i}-\hat{j}-\hat{k}$. Then the vector $\overline{b}$ satisfying $\overline{a} \times \overline{b}+\overline{c}=\overline{0}$ and $\overline{a} \cdot \overline{b}=3$,is

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