Question

If $\mathbf { a } = \mathbf { i } + \mathbf { j } + \mathbf { k } , \mathbf { b } = \mathbf { i } + \mathbf { j } , \mathbf { c } = \mathbf { i }$ and $( \mathbf { a } \times \mathbf { b } ) \times \mathbf { c } = \lambda \mathbf { a } + \mu \mathbf { b }$, then $\lambda + \mu =$

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

0

Answer 2

$( \mathbf { a } \times \mathbf { b } ) \times \mathbf { c } = \lambda \mathbf { a } + \mu \mathbf { b }$

̃ $( \mathbf { a } \cdot \mathbf { c } ) \mathbf { b } - ( \mathbf { b } \cdot \mathbf { c } ) \mathbf { a } = \lambda \mathbf { a } + \mu \mathbf { b }$ ̃ $\lambda = - \mathbf { b } . \mathbf { c }$ ,

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

=