If a → ,   b → ,   c → are unit vectors such that a → + 2 b → + 2 c…

If a→, b→, c→ are unit vectors such that a→+2b→+2c→=0→, then a→×c→ is equal to :
  1. 14
  2. 1516
  3. 154 
  4. 1516

Solution

Given a→+2b→+2c→=0

⇒a→+2c→=-2b→

Squaring both sides,

⇒a→2+4c→2+4a→.c→=4b→2

⇒1+4+4cos⁡θ=4⇒cos⁡θ=-14

∴sin⁡θ=1-cos2⁡θ=154

Now, a→×c→=a→c→sin⁡θ=154

Asked in: JEE Main 2018 (15 Apr)

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