First slide

Scalars and Vectors

Question

Three vectors $\vec{A}, \vec{B} and \vec{C}$ satisfy the relation $\vec{A} \cdot \vec{B} = 0 and \vec{A} \cdot \vec{C} = 0$ . 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

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

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