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Vector Notation

If a1, b1, c1...

Question

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

A

0

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B

1

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C

2

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D

3

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Solution

The correct option is A $0$
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 $\to a .^{1} + \to b .^{1} + \to c .^{1} = \to a . \frac{(\to c \times \to a)}{[\to a \to b \to c]} + \to b . \frac{(\to a \times \to b)}{[\to a \to b \to c]} + \to c . \frac{(\to b \times \to c)}{[\to a \to b \to c]}$
$= 0 + 0 + 0 = 0$

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\to a =^i +^j +^k, \to b = 2^i +^k, \to c =^i + 2^j + 3^k

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Vector Notation

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