Question

$\bar{A},\bar{B},\bar{C}$are three vectors respectively given by $2\widehat{i} + \widehat{k}$, $\widehat{i} + \widehat{j} + \widehat{k}$,and $4\widehat{i} - 3\widehat{j} + 7\widehat{k}$. Then vector$\bar{R}$, which satisfies the relation$\bar{R}\ \times \bar{B} = \bar{C} \times \bar{B}and\bar{R}.\bar{A} = 0$, is

• A. $2\widehat{i} - 5\widehat{j} + 2\widehat{k}$
• B. $- \widehat{i} + 4\widehat{j} + 2\widehat{k}$
• C. $- \widehat{i} - 8\widehat{j} + 2\widehat{k}$
• D. None of these

Answer 1

Answer: (C)

$- \widehat{i} - 8\widehat{j} + 2\widehat{k}$

Answer 2

We have $\bar{R}\ \times \bar{B} = \bar{C} \times \bar{B}and\bar{R}.\bar{A} = 0$

⇒ $\bar{A}\ \times \left( \bar{R} \times \bar{B} \right) = \bar{A} \times \left( \bar{C} \times \bar{B} \right)$

⇒ $\left( \bar{A}.\bar{B} \right)\bar{R} - \left( \bar{A}.\bar{R} \right)\bar{B} = \left( \bar{A}.\bar{B} \right)\bar{C} - \left( \bar{A}.\bar{C} \right)\bar{B}$⇒ (2 +1)$\bar{R}$ = 3$\bar{C}$ – ( 8+7) $\bar{B}$ ⇒ $\bar{R}$ = $\bar{C} - 5\bar{B} = - \widehat{i} - 8\widehat{j} + 2\widehat{k}$