Question

If $\mathbf { a } = \mathbf { i } - \mathbf { j }$ and $\mathbf { b } = \mathbf { i } + \mathbf { k }$, then a unit vector coplanar with a and b and perpendicular to a is

• A. i
• B. j
• C. k
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\mathbf { c } = \lambda \mathbf { a } + \mu \mathbf { b } = ( \lambda + \mu ) \mathbf { i } - \lambda \mathbf { j } + \mu \mathbf { k }$

Now,

Therefore, $\mathbf { c } = - \lambda \mathbf { i } - \lambda \mathbf { j } - 2 \lambda \mathbf { k } = ( \sqrt { 6 } ) ( - \lambda ) \left[ \frac { \mathbf { i } + \mathbf { j } + 2 \mathbf { k } } { \sqrt { 6 } } \right]$

Hence, unit vector $= \frac { ( \mathbf { i } + \mathbf { j } + 2 \mathbf { k } ) } { \sqrt { 6 } }$.