a·b×ii+a·b×jj+a·b×kk=

a×b·i i +a×b·j j+a×b·k k a × b = xi + yj + zkxi+yj+zk=a×b

a·b×ii+a·b×jj+a·b×kk=

a×b·i i +a×b·j j+a×b·k k a × b = xi + yj + zkxi+yj+zk=a×b

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$\{a \cdot (b \times i)\} i + \{a \cdot (b \times j)\} j + \{a \cdot (b \times k)\} k =$

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$b \times a$

$a + b$

$a - b$

$a \times b$

answer is B.

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Detailed Solution

$[(a \times b) \cdot i] i + (a \times b \cdot j) j + (a \times b \cdot k) k \begin{array}{rcl} a \end{array} \begin{array}{rcl} \times \end{array} \begin{array}{rcl} b \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} xi \end{array} \begin{array}{rcl} + \end{array} \begin{array}{rcl} yj \end{array} \begin{array}{rcl} + \end{array} \begin{array}{rcl} zk \end{array}$