If a-b-c-a-b-c- then one of the condition

The correct option is A a,c are parallel #10; a⃗× (b⃗×c⃗)=(a⃗.c⃗)b⃗ (a⃗ b⃗)c⃗ #160; #160; #160; #160; #160; (1) (a⃗×b⃗)×c⃗=(a⃗ ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a×b×c=a×...

Question

If $¯ ¯ ¯ a \times (¯ ¯ b \times ¯ ¯ c) = (¯ ¯ ¯ a \times ¯ ¯ b) \times ¯ ¯ c$ , then one of the condition

¯ ¯ ¯ a, ¯ ¯ c

are parallel

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¯ ¯ ¯ a, ¯ ¯ b

are parallel

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¯ ¯ b, ¯ ¯ c

are parallel

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¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

are parallel

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Solution

The correct option is A $¯ ¯ ¯ a, ¯ ¯ c$ are parallel
$\to a \times (\to b \times \to c) = (\to a . \to c) \to b - (\to a - \to b) \to c$ -(1)
$(\to a \times \to b) \times \to c = (\to a - \to c) \to b - \to a (\to c - \to b) \to a$ --(2)
equal (1) & (2)
$- (\to a - \to b) \to c = - (\to c - \to b) \to a$
$(\to a - \to b) \to c = - (\to c \to b) \to a$
$\to c = \frac{(\to c - \to b)}{\to a - \to b} \to a$
$\to c = k \to a$
So $\to c | | \to a$

Suggest Corrections

Similar questions

If a, b, c, d are unit vectors such that (axb).(cxd)=1 and a.c=1/2 then

a) a, b, c are non-coplanar

b) b, c, d are non-coplanar

c) b, d are non-parallel

d) a, dare parallel and b, c are parallel

Q. If

a

b

and

c

are three non-zero vectors such that

a . | b \times c | = 0

and

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Q. If

a, b, c

are three unit vectors such that

a \times (b \times c) = \frac{1}{2} b

and

c

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\to a, \to b, \to c

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and

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then:

a, b, c

are three unit vectors such that

a \times (b \times c) = \frac{1}{2} (b + c)

. If the vectors

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If ¯¯¯a×(¯¯b×¯¯c)=(¯¯¯a×¯¯b)×¯¯c, then one of the condition

If $¯ ¯ ¯ a \times (¯ ¯ b \times ¯ ¯ c) = (¯ ¯ ¯ a \times ¯ ¯ b) \times ¯ ¯ c$ , then one of the condition