If a, b, c are non-coplanar then find the value of 2[a b c] + [b a c] =

  1. [c b a]
  2. [a b c]
  3. 2[a b c]
  4. 0

Answer (Detailed Solution Below)

Option 2 : [a b c]
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Detailed Solution

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Concept:

  • If a, b, c are coplanar then [a b c] = 0
  • Three vectors are permuted in the same cyclic order, the value of the scalar triple product remains the same. ⇒  [a b c] = [b c a] = [c a b]


Calculation:

Here, a, b, c are non-coplanar

To find: 2[a b c] + [b a c] =?

⇒ 2[a b c] + [b a c]

= 2 [a, b, c] - [a, b, c]                (∵ [b a c] = -[a b c])

= [a, b, c] 

Hence, option (2) is correct.

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