First slide

Vectors

Question

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

Moderate

A

$\vec{A} \times \vec{B}$
B

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

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

$\vec{B} and \vec{C}$

Solution

$Vector triple product of three vectors \vec{A}, \bar{B} and \bar{C} is \vec{A} \times (\vec{B} \times \vec{C}) = (\vec{A} \cdot \vec{C}) \vec{B} - (\vec{A} \cdot \vec{B}) \vec{C} Given : \vec{A} \cdot \bar{B} = 0, \vec{A} \cdot \vec{C} = 0 ∴ \vec{A} \times (\bar{B} \times \vec{C}) = 0 Thus the vector \vec{A} is parallel to vector \vec{B} \times \vec{C} .$

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