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Intersection of Sets

If a,b,c and ...

Question

If $\to a, \to b, \to c$ and $\to p, \to q, \to r$ are sets of three non-coplanar unit vectors such that $\to a \cdot \to p + \to b \cdot \to q + \to c \cdot \to r = 3,$ then vectors $\to p, \to q$ and $\to r$ respectively are given by the vectors

A

\frac{\to a \times \to b}{[\to a \to b \to c]}, \frac{\to b \times \to c}{[\to a \to b \to c]}, \frac{\to c \times \to a}{[\to a \to b \to c]}

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B

\to b \times \to c, \to c \times \to a, \to a \times \to b

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C

\to a \times \to b, \to b \times \to c, \to c \times \to a

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D

\frac{\to b \times \to c}{[\to a \to b \to c]}, \frac{\to c \times \to a}{[\to a \to b \to c]}, \frac{\to a \times \to b}{[\to a \to b \to c]}

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Solution

The correct option is D $\frac{\to b \times \to c}{[\to a \to b \to c]}, \frac{\to c \times \to a}{[\to a \to b \to c]}, \frac{\to a \times \to b}{[\to a \to b \to c]}$
Given :
$\to a \cdot \to p + \to b \cdot \to q + \to c \cdot \to r = 3$
Possible if , $\to a \cdot \to p = \to b \cdot \to q = \to c \cdot \to r = 1$
$\Rightarrow \to p, \to q, \to r$ are reciprocals of $\to a, \to b, \to c$ respectively.
$\Rightarrow \to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]}$

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Intersection of Sets

Standard XII Mathematics

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