First slide

Vectors

Question

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

Moderate

A

$\vec{B}$
B

$\vec{C}$
C

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

$\vec{B} + \vec{C}$

Solution

If $\vec{A} . \vec{B} = 0, \vec{A} is perpendicular to \vec{B .}$
$If \vec{A} . \vec{C} = 0, \vec{A} is perpendicular to \vec{C .}$
So $\vec{A} is perpendicular to both \vec{B} and \vec{C} .$
Also $\vec{B} \times \vec{C} is perpendicular to both \vec{B} and \vec{C}$
Hence $\vec{A} is parallel to \vec{B} \times \vec{C} .$

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