if|A vector.B vector|= |A vector×B vector|, find the angle between A vector and B vector
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Notice, a⃗ ×b⃗ & b⃗ ×a⃗ are equal in magnitude & opposite in direction hence the angle between a⃗ ×b⃗ & b⃗ ×a⃗ is π or 180∘
OR
Mathematically, we know that a⃗ ×b⃗ =−b⃗ ×a⃗
∴(a⃗ ×b⃗ )⋅(b⃗ ×a⃗ )=(a⃗ ×b⃗ )⋅(−a⃗ ×b⃗ )
|a⃗ ×b⃗ ||b⃗ ×a⃗ |cosθ=−(a⃗ ×b⃗ )⋅(a⃗ ×b⃗ )
|a⃗ ×b⃗ ||a⃗ ×b⃗ |cosθ=−|a⃗ ×b⃗ |2
|a⃗ ×b⃗ |2cosθ=−|a⃗ ×b⃗ |2
cosθ=−1
cosθ=cosπ
θ=π or 180∘
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