First slide

Scalar triple product of vectors

Question

If $\vec{a} = \hat{i} + \hat{j}, \vec{b} = \hat{j} + \hat{k}, \vec{c} = \hat{k} + \hat{i}$ then in the reciprocal system of vectors $\vec{a}, \vec{b}, \vec{c}$ reciprocal of vector $\vec{a}$ is

Moderate

A

$\frac{\hat{i} + \hat{j} + \hat{k}}{2}$
B

$\frac{\hat{i} - \hat{j} + \hat{k}}{2}$
C

$\frac{- \hat{i} - \hat{j} + \hat{k}}{2}$
D

$\frac{\hat{i} + \hat{j} - \hat{k}}{2}$

Solution

$\vec{a^{'}} = \frac{\vec{b} \times \vec{c}}{[\vec{a} \vec{b} \vec{c}]} = \frac{\hat{i} + \hat{j} - \hat{k}}{2}$

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