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Intersection of Sets

If a1, b1, c1...

Question

If $^{1},^{1},^{1}$ is the reciprocal system of vector triad of $\to a, \to b, \to c$ , then $\to a \times^{1} + \to b \times^{1} + \to c \times^{1}$ is:

A

\to 0

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B

\to a

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C

\to b

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D

\to c

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Solution

The correct option is A $\to 0$
We know, for the reciprocal system, $^{1} = \frac{\to b \times \to c}{[\to a \to b \to c]}$
Similarly, $^{1} = \frac{\to c \times \to a}{[\to a \to b \to c]}$
and $^{1} = \frac{\to a \times \to b}{[\to a \to b \to c]}$
Hence $\to a \times^{1} + \to b \times^{1} + \to c \times^{1} = Σ \to a \times \frac{(\to b \times \to c)}{[\to a \to b \to c]} = \frac{[(\to a \cdot \to c) \to b - (\to a \cdot \to b) \to c] + [(\to b \cdot \to a) \to c - (\to b \cdot \to c) \to a] + [(\to c \cdot \to b) \to a - (\to c \cdot \to a) \to b]}{[\to a \to b \to c]} = 0$

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Intersection of Sets

Standard XII Mathematics

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