If a-b-c-b - a- bb - c - - a - c- then - is equal to

Scalar product of four vectors (a×b).(c×b) =(a. c)(b . b) nbsp;(a. b)(b . c) Hence, (a×b).(c×b) + (a. b)(b . c) = |b|^2 (a . c) comparing with, (a×b).(c×b) ...

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Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

If a×b.c×b + ...

Question

If $(\to a \times \to b) . (\to c \times \to b) + (\to a . \to b) (\to b . \to c) = λ (\to a . \to c),$ then $λ$ is equal to

| \to a |^{2}

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| \to b |^{2}

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| \to c |^{2}

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Solution

The correct option is B $| \to b |^{2}$
Scalar product of four vectors
$(\to a \times \to b) . (\to c \times \to b) = (\to a . \to c) (\to b . \to b) - (\to a . \to b) (\to b . \to c)$
Hence,
$(\to a \times \to b) . (\to c \times \to b) + (\to a . \to b) (\to b . \to c) = | \to b |^{2} (\to a . \to c)$
comparing with,
$(\to a \times \to b) . (\to c \times \to b) + (\to a . \to b) (\to b . \to c) = λ (\to a . \to c)$
$∴ λ = | \to b |^{2}$

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Scalar Triple Product

Standard XII Mathematics

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