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) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

| \to b |^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

| \to c |^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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,
$(\to a \times \to b) . (\to c \times \to b) + (\to a . \to b) (\to b . \to c) = λ (\to a . \to c)$
$∴ λ = | \to b |^{2}$

Suggest Corrections

Similar questions

Q. If

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

, then

λ

is equal to

Q. If

\to a \times (\to b \times \to c) + \to b \times (\to c \times \to a) = λ_{1} \to a + λ_{2} \to b + λ_{3} \to c

then

λ_{1} + λ_{2} + λ_{3} =

Q. If

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

then

λ

is equal to

Q. If

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

then

λ

is equal to

Q. Let

\to a, \to b

and

\to c

be three unit vectors such that

\to a + \to b + \to c = \to 0

. If

λ = \to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a

and

\to d = \to a \times \to b + \to b \times \to c + \to c \times \to a

, then the ordered pair

(λ, \to d)

is equal to:

Join BYJU'S Learning Program

Explore more

Scalar Triple Product

Standard XII Mathematics

Join BYJU'S Learning Program

If (→a×→b).(→c×→b)+(→a.→b)(→b.→c)=λ(→a.→c), then λ is equal to

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