Let A-b-c- B-c-a- C-a-b- then the vectors A-B-C- B-C-A- and C-A-B- are

The correct option is C CoplanarWe have #160; A× (B× #160;C) = (A.C)B (A.B)C #160; Similarly if other terms are also solved, we will get all the te ...

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Standard XII

Mathematics

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Let A⃗=b⃗×c...

Question

Let $\to A = \to b \times \to c, \to B = \to c \times \to a, \to C = \to a \times \to b$ , then the vectors $\to A \times (\to B \times \to C)$ , $\to B \times (\to C \times \to A)$ , and $\to C \times (\to A \times \to B)$ are

Collinear

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Coplanar

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Non-coplanar

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Non-collinear

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Solution

The correct option is C Coplanar
We have
$¯ ¯¯ ¯ A \times (¯ ¯¯ ¯ B \times ¯ ¯¯ ¯ C) = (¯ ¯¯ ¯ A . ¯ ¯¯ ¯ C) ¯ ¯¯ ¯ B - (¯ ¯¯ ¯ A . ¯ ¯¯ ¯ B) ¯ ¯¯ ¯ C$
Similarly if other terms are also solved, we will get all the terms in terms of $¯ ¯¯ ¯ A, ¯ ¯¯ ¯ B, ¯ ¯¯ ¯ C .$
Assuming $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are coplanar, we get thus that the above three vectors are coplanar.

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Similar questions

Q. If

\to a, \to b, \to c

are non-zero non-collinear vectors such that

\to a \times \to b = \to b \times \to c = \to c \times \to a

, then

\to a + \to b + \to c =

Q. Let

| \to a | = 1, ∣ ∣ \to b ∣ ∣ = \sqrt{2}

| \to c | = \sqrt{3}

, and

\to a ⊥ (\to b + \to c)

\to b ⊥ (\to c + \to a)

and

\to c ⊥ (\to a + \to b)

, then

∣ ∣ \to a + \to b + \to c ∣ ∣

Q. If

\to a, \to b, \to c

are three vectors such that

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

then prove that

| \to a | = | \to b | = | \to c |

Q. Let

\to a =^i +^j +^k

\to b = - 3^i +^k

and

\to c =^i + 2^j + 3^k

, then the ascending order of magnitudes of

A)

[\to a \times \to b

\to b \times \to c

\to c \times \to a]

B)

[\to a + \to b

\to b + \to c

\to c + \to a]

C)

[\to a

\to b

\to c]

[\to a

\to b

\to c]^{- 1}

D)

[\to a - \to b

\to b - \to c

\to c - \to a]

(\to a + \to b) \times (\to a - \to b) + (\to b + \to c) \times (\to b - \to c) + (\to c + \to a) \times (\to c - \to a) =

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Let →A=→b×→c, →B=→c×→a, →C=→a×→b, then the vectors →A×(→B×→C), →B×(→C×→A), and→C×(→A×→B) are

Let $\to A = \to b \times \to c, \to B = \to c \times \to a, \to C = \to a \times \to b$ , then the vectors $\to A \times (\to B \times \to C)$ , $\to B \times (\to C \times \to A)$ , and $\to C \times (\to A \times \to B)$ are