Three vectors A→,B→ and C→ satisfy the relation A→.B→=0 and A→.C→=0. The vector A is Parallel to :

Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ satisfy the relation $\vec{A} . \vec{B}$ =0 and $\vec{A} . \vec{C}$ =0. The vector A is Parallel to :

A
$\vec{B}$
B
$\vec{C}$
C
$\vec{B} . \vec{C}$
D
$\vec{B} \times \vec{C}$

Solution:

$\vec{A} . \vec{B}$ =0 $\Rightarrow \vec{A} ⊥ \vec{B}$ and $\vec{A} . \vec{C}$ =0 $\vec{A} ⊥ \vec{C}$

$∴$ $\vec{A}$ is parallel to $\vec{B} \times \vec{C}$ .

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