If a- b- c are non-zero- non-coplanar vectors then a-b-c-b-c-a is collinear with the vectors

{a×(b+c)}×{b×(c a)} ={a×b+a×c}×{b×c b×a} ={a×b c×a}×{b×c+a×b} =(a×b)×(b×c)+(a×b)×(a×b) (c×a)×(b×c) (c×a)×(a×b) =[a b c]b [a b b]c+[a b b]a [a b a]b [c a ...

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Byju's Answer

Standard XII

Mathematics

Intersection of Sets

If a, b, c ar...

Question

If $\to a, \to b, \to c$ are non-zero, non-coplanar vectors then ${\to a \times (\to b + \to c)} \times {\to b \times (\to c - \to a)}$ is collinear with the vector(s)

\to a + \to b + \to c

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- \to a + \to b + \to c

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- \to a - \to b - \to c

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\to a - \to b - \to c

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Solution

The correct option is D $\to a - \to b - \to c$
${\to a \times (\to b + \to c)} \times {\to b \times (\to c - \to a)} = {\to a \times \to b + \to a \times \to c} \times {\to b \times \to c - \to b \times \to a} = {\to a \times \to b - \to c \times \to a} \times {\to b \times \to c + \to a \times \to b} = (\to a \times \to b) \times (\to b \times \to c) + (\to a \times \to b) \times (\to a \times \to b) - (\to c \times \to a) \times (\to b \times \to c) - (\to c \times \to a) \times (\to a \times \to b) = [\to a \to b \to c] \to b - [\to a \to b \to b] \to c + [\to a \to b \to b] \to a - [\to a \to b \to a] \to b - [\to c \to a \to c] \to b + [\to c \to a \to b] \to c - [\to c \to a \to b] \to a + [\to c \to a \to a] \to b = [\to a \to b \to c] (\to b + \to c - \to a)$
So given vector is collinear with $\pm (\to a - \to b - \to c)$

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Similar questions

Q. Let

\to a, \to b, \to c

be three non zero vectors which are pairwise non-collinear. If

\to a + 3 \to b

is collinear and

\to b + 2 \to c

is collinear with

\to a

, then

\to a + 3 \to b + 6 \to c

Let $\to a, \to b$ and $\to c$ be three non -zero vectors such that they are mutually non collinear. If the vector $\to a + 2 \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ then $\to a + 2 \to b + 6 \to c$ equals