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Test for Collinearity of Vectors

If [ a⃗×b⃗ ...

Question

If $[\to a \times \to b \to b \times \to c \to c \times \to a] = λ {[\begin{matrix} \to a & \to b & \to c \end{matrix}]}^{2}$ then $λ$ is equal to

A

0

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B

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C

2

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D

3

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Solution

The correct option is C 1
$\begin{matrix} [\to a \times \to b \to b \times \to c \to c \times \to a] (\to a \times \to b) . [(\to b \times \to c) \times (\to c \times \to a)] (\to a \times \to b) . [[\to b \to c \to a] \to c - [\to b \to c \to c] \to a] = {[\to a \to b \to c]}^{2} ∴ λ = 1 H e n c e, t h e o p t i o n B i s c o r r e c t a n s w e r . \end{matrix}$

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Similar questions

[\to a \to b \to c] = \to k

k \neq 0

[(\to b \times \to c) \times (\to c \times \to a) (\to c \times \to a) \times (\to a \times \to b) (\to a \times \to b) \times (\to b \times \to c)] =

[\to a \to b \to c] = 2

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

[\to a \times \to b \to b \times \to c \to c \times \to a] = λ {[\to a \to b \to c]}^{2}

λ

\frac{[(\to a \times \to b) \times (\to b \times \to c) (\to b \times \to c) \times (\to c \times \to a) (\to c \times \to a) \times (\to a \times \to b)]}{[\to a \times \to b \to b \times \to c \to c \times \to a]}

4 \to a + 5 \to b + 9 \to c = 0

(\to a \times \to b) \times [(\to b \times \to c) \times (\to c \times \to a)]

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