If - a - b b - c c - a - a b c -2 then - is equal toA- 2B- 3C- 0D-

[a×b b×c c×a] =(a×b).{(b×c)×(c×a)} =(a×b).([b c a] c [ b c c] a) =[ b c a][ a b c] =[ a b c]^2 Hence, λ = 1 ...

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

Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

If [ a × b b ...

Question

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

2

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

3

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!

1

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

Open in App

Solution

The correct option is D $1$
$[\to a \times \to b \to b \times \to c \to c \times \to a] = (\to a \times \to b) . {(\to b \times \to c) \times (\to c \times \to a)}$
$= (\to a \times \to b) . ([\to b \to c \to a] \to c - [\to b \to c \to c] \to a)$
$= [\to b \to c \to a] [\to a \to b \to c]$
$= [\to a \to b \to c]^{2}$
Hence, $λ = 1$

Suggest Corrections

Similar questions

Q. If

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

, then

λ =

If z = x + iy, $z^{\frac{1}{3}}$ = a - ib and $\frac{x}{a}$ - $\frac{y}{b}$ = $λ$ $(a^{2} - b^{2})$ , then $λ$ is equal to

Q. If three points (0, 0),

(3, \sqrt{3})

and (3, λ) form an equilateral triangle, then λ =

(a) 2

(b) −3

(c) −4

(d) None of these

Let $f (x) = x^{3} + \frac{1}{x^{3}}, x \neq 0$ . If the intervals in which f(x) increases are $(- \infty, a]$ and $[b, \infty)$ then min(b - a) is equal to

a b c + b c a + c a b - 3 a b c =

Join BYJU'S Learning Program

If [→a×→b →b×→c →c×→a]=λ[→a →b →c]2 then λ is equal to

The correct option is D 1[→a×→b →b×→c →c×→a]=(→a×→b).{(→b×→c)×(→c×→a)} =(→a×→b).([→b →c →a]→c−[→b →c →c]→a) =[→b →c →a][→a →b →c] =[→a →b →c]2 Hence, λ=1

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