If a → and b → are two vectors such that a → · b → | a → | | b → |…

If a→ and b→ are two vectors such that a→·b→|a→||b→|<0 and |a→·b→|=|a→×b→|, then the angle between the vectors a→ and b→ is
  1. π4
  2. sec−1⁡(−2)
  3. tan−1⁡−12
  4. sin−1⁡12.

Solution

Given, |a→·b→|=|a→×b→|

⇒a→b→cosθ=a→b→sinθ, where θ is the angle between vectors a and b.

⇒cosθ=sinθ

⇒θ=π4 or 3π4

But, given that a→·b→|a→||b→|<0

⇒cosθ<0

Hence θ=3π4 or sec-1-2.

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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