Let a → = i ^ - j ^ ,     b → = i ^ + j ^ + k ^ and c → be a vector such that a…

Let a→=i^-j^,  b→=i^+j^+k^ and c→ be a vector such that a→×c→+b→=0→ and a→.c→=4, then |c→|2 is equal to:
  1. 192
  2. 9
  3. 172
  4. 8

Solution

Let the angle between a→ and c→ is θ.

∴  cos⁡θ=a→ . c→a→ c→=42 c→

Given, a→×c→+b→=0

⇒  a→×c→=b→

⇒  a→. c→sin⁡θ=b→

⇒   a→2c→2sin2⁡θ=b→2

⇒  2c→21-cos2⁡θ=3

⇒  2c→21-162c→2=3

⇒  2c→2-16=3

⇒   c→2=192

Asked in: JEE Main 2019 (09 Jan Shift 1)

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