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Condition for Coplanarity of Four Points

If b and ...

Question

If $\to b$ and $\to c$ are two perpendicular unit vectors and $\to a$ is any vector, then $(\to a . \to b) \to b + (\to a . \to c) \to c + \frac{\to a (\to b \times \to c)}{{∣ ∣ ∣ \to b \times \to c ∣ ∣ ∣}^{2}} (\to b \times \to c)$ is equal to

A

\to a

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B

\to b

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C

\to c

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D

None of these

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Solution

The correct option is A None of these
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b

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are any two non-collinear unit vectors and

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is any vector, then

(a . b) b + (a . c) + \frac{a . b \times c}{| b \times c |} . (b \times c)

b

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a

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(a \cdot b) b + (a \cdot c) c + \frac{a \cdot (b \times c)}{{| b \times c |}^{2}} (b \times c)

\to b

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(\to a, \to b) \to b + (\to a . \to c) \to c + \frac{\to a . (\to b \times \to c)}{∣ ∣ ∣ \to b \times \to c ∣ ∣ ∣} (\to b \times \to c) =

b

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are three non-coplanar vectors, then

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Condition for Coplanarity of Four Points

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