If a → , b → , c → are non coplanar non - zero vectors such that b → × c → = a → , a → × b → = c → and c → × a → = b → , then which of the following is not true

Question

If a → , b → , c → are non coplanar non - zero vectors such that b → × c → = a → , a → × b → = c → and c → × a → = b → , then which of the following is not true, a → = 1, a → b → c → = 1, a → + b → + c → = 3, a → ≠ b → ≠ c →

MARKS App · Accepted Answer

b → × c → = a → ⇒ a → b → c → = a → . a → = a → 2 Similarly, a → b → c → = b → 2 = c → 2 ∴ a → = b → = c → = a → b → c → Now, b → × c → c → × a → a → × b → = a → b → c → 2 ∴ a → b → c → = a → b → c → 2 But, a → b → c → ≠ 0 (non-coplanar) So a → b → c → = 1 Hence a → = b → = c → = 1

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