Question

If V3|Ā x B = A-B, then find the angle between A and B.​

Answer 1

Given that

A⃗ +B⃗ =A⃗ −B⃗  

Taking self dot product on both the sides we get

(A⃗ +B⃗ )⋅(A⃗ +B⃗ )=(A⃗ −B⃗ )⋅(A⃗ −B⃗ )

A⃗ ⋅A⃗ +A⃗ ⋅B⃗ +A⃗ ⋅B⃗ +B⃗ ⋅B⃗ =A⃗ ⋅A⃗ −A⃗ ⋅B⃗ −A⃗ ⋅B⃗ +B⃗ ⋅B⃗  

A2+2A⃗ ⋅B⃗ +B2=A2−2A⃗ ⋅B⃗ +B2

2A⃗ ⋅B⃗ =−2A⃗ ⋅B⃗  

A⃗ ⋅B⃗ =0

ABcosθ=0

cosθ=0

θ=90∘

hence, two vectors A⃗  & B⃗  are perpendicular to each other

Hope helps

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