If [a×bb×cc×a]=λ[abc]2, then λ is equal to?
0
1
2
3
Explanation for the correct option:
Find the value of λ:
Given, [a×bb×cc×a]=λ[abc]2
Take L.H.S of the equation
[a×bb×cc×a]=(a×b)·(b×c)×(c×a)
=(a×b)([bca]c−[bcc]a) ∵(a×b)×(c×d)=[abd]c−[abc]d
=(a×b)([bca]c) ∵[bcc]=0
=(a×b)·c[bca]
=[abc][bca]
=[abc]2 ∵[bca]=[abc]=[cab]
=R.H.S
∴λ=1
Hence, Option ‘B’ is Correct.