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If $a^{1}, b^{1}, c^{1}$ represents the reciprocal system of vectors $a, b, c$ then $a \cdot a^{1} + b \cdot b^{1} + c \cdot c^{1} =$

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answer is D.

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Detailed Solution

$\begin{array}{rcl} = & a \cdot (\frac{b \times c}{[a b c]}) + b \cdot (\frac{c \times a}{[a b c]}) + c \cdot (\frac{a \times b}{[a b c]}) \\ = & 1 + 1 + 1 = 3 \end{array}$

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