Question

If $\mathbf { p } = \mathbf { i } - 2 \mathbf { j } + 3 \mathbf { k }$ and $\mathbf { q } = 3 \mathbf { i } + \mathbf { j } + 2 \mathbf { k }$ then a vector along r which is linear combination of p and q and also perpendicular to q is

• A. $\mathbf { i } + 5 \mathbf { j } - 4 \mathbf { k }$
• B. $\mathbf { i } - 5 \mathbf { j } + 4 \mathbf { k }$
• C. $- \frac { 1 } { 2 } ( \mathbf { i } + 5 \mathbf { j } - 4 \mathbf { k } )$
• D. None of these

Answer 1

Answer: (C)

$- \frac { 1 } { 2 } ( \mathbf { i } + 5 \mathbf { j } - 4 \mathbf { k } )$

Answer 2

$\mathbf { r } = \mathbf { p } + \lambda \mathbf { q } \Rightarrow \mathbf { r } \cdot \mathbf { q } = \mathbf { p } \cdot \mathbf { q } + \lambda \mathbf { q } \cdot \mathbf { q }$

$\Rightarrow 0 = 7 + 14 \lambda \Rightarrow \lambda = - \frac { 1 } { 2 }$

Therefore, $\mathbf { r } = - \frac { 1 } { 2 } ( \mathbf { i } + 5 \mathbf { j } - 4 \mathbf { k } )$