Let a → and b → be two non-zero vectors perpendicular to each other and | a → | = | b…

Let a→ and b→ be two non-zero vectors perpendicular to each other and |a→|=|b→|, If |a→×b→|=|a→|, then the angle between the vectors
(a→+b→+(a→×b→)) and a→ is equal to :
  1. sin-113
  2. cos-113
  3. cos-112
  4. sin-116

Solution

|a→|=|b→|,|a→×b→|=|a→|,a→⊥b→

|a→×b→|=|a→|⇒|a→||b→|sin90°=|a→|⇒|b→|=1=|a→|

a→ and b→ are mutually perpendicular unit vectors.

Let a→=i^,b→=j^⇒a→×b→=k^

cosθ=(i^+j^+k^)i^31=13⇒θ=cos-113

Asked in: JEE Main 2021 (18 Mar Shift 2)

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