Question

if|A vector.B vector|= |A vector×B vector|, find the angle between A vector and B vector​

Answer 1

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∘

$\bf \red{Khushi}$