A - b - c - b - c - a - c - a - b areA- CollinearB- coplanarC- Non-coplanar- non-collinearD- None of the above

The correct option is B coplanar Let p=a⃗× (b⃗×c⃗) q=b⃗× (c⃗×a⃗) r=c⃗× (a⃗×b⃗) p+q+r= a⃗× (b⃗×c⃗)+b⃗× (c⃗×a⃗)+c⃗× (a⃗×b⃗) = (a . c) – (a . b)c + (b . a)c – (b ...

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Byju's Answer

Standard X

Mathematics

Vector Triple Product

a × b × c , b...

Question

$\to a \times (\to b \times \to c), \to b \times (\to c \times \to a), \to c \times (\to a \times \to b)$ are

Collinear

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coplanar

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Non-coplanar, non-collinear

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None of the above

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Solution

The correct option is B coplanar
Let $p = \to a \times (\to b \times \to c)$
$q = \to b \times (\to c \times \to a)$
$r = \to c \times (\to a \times \to b)$
$p + q + r = \to a \times (\to b \times \to c) + \to b \times (\to c \times \to a) + \to c \times (\to a \times \to b)$
= {(a . c) – (a . b)c} + {(b . a)c – (b . c)a} + {(c . b)a – (c . a)b}
= {(a . c)b – (a . b)c + (a . b)c – (b . c)a + (b . c)a – (a . c)b}
= 0
So p + q + r = 0
or $p = (- 1) \times q + (- 1) \times r$
So p is a linear combination of q and r.
So they are coplanar.

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