Question

Let $\mathbf { a } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$ and $\mathbf { b } = \mathbf { i } + \mathbf { j }$ If c is a vector such that and the angle between $( \mathbf { a } \times \mathbf { b } )$ and c is $30 ^ { \circ }$, then $| ( \mathbf { a } \times \mathbf { b } ) \times \mathbf { c } | =$

• A. $\frac { 2 } { 3 }$
• B. $\frac { 3 } { 2 }$
• C. 2
• D. 3

Answer 1

Answer: (B)

$\frac { 3 } { 2 }$

Answer 2

$\mathbf { a } \times \mathbf { b } = \left| \begin{array} { c c c } \mathbf { i } & \mathbf { j } & \mathbf { k } \\ 2 & 1 & - 2 \\ 1 & 1 & 0 \end{array} \right| = 2 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }$

$\therefore | \mathbf { a } \times \mathbf { b } | = \sqrt { 4 + 4 + 1 } = 3$

$| \mathbf { c } - \mathbf { a } | = 2 \sqrt { 2 } \Rightarrow | \mathbf { c } - \mathbf { a } | ^ { 2 } = ( \mathbf { c } - \mathbf { a } ) ^ { 2 } = 8$

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