Question

The vector equation of the line joining the points $\mathbf { i } - 2 \mathbf { j } + \mathbf { k }$ and $- 2 \mathbf { j } + 3 \mathbf { k }$ is

• A. $\mathbf { r } = t ( \mathbf { i } + \mathbf { j } + \mathbf { k } )$
• B. $\mathbf { r } = t _ { 1 } ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } ) + t _ { 2 } ( 3 \mathbf { k } - 2 \mathbf { j } )$
• C. $\mathbf { r } = ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } ) + t ( 2 \mathbf { k } - \mathbf { i } )$
• D. $\mathbf { r } = t ( 2 \mathbf { k } - \mathbf { i } )$

Answer 1

Answer: (C)

$\mathbf { r } = ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } ) + t ( 2 \mathbf { k } - \mathbf { i } )$

Answer 2

Vector equation of a straight line passing through two points a and b is, $\mathbf { r } = \mathbf { a } + t ( \mathbf { b } - \mathbf { a } )$

⇒ $\mathbf { r } = ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } ) + t ( 2 \mathbf { k } - \mathbf { i } )$