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$The unit vector orthogonal to a = 2 i + 2 j + k, b = 3 j + 4 j - 12 k and forming a right handed system with a and b is$

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$i + j + k$

$- 28 i + 27 j + 2 k$

$j + k - i$

$\frac{- 28 i + 27 j + 2 k}{\sqrt{1517}}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} a \times b & = & |\begin{matrix} i & j & k \\ 2 & 2 & 1 \\ 3 & 4 & - 12 \end{matrix}| = i (- 28) - j (- 27) + k (2) \\ | a \times b | & = & \sqrt{{(28)}^{2} + {(27)}^{2} + 4} = \sqrt{1517} \end{array}$

Unit vector $= \frac{- 28 i + 27 j + 2 k}{\sqrt{1517}}$

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