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For any two vectors u and v, prove that ∣u×v∣2+(u⋅v)2=∣u∣2∣v∣2.
The obtuse triangle OAB has area 2 and OA⃗⋅OB⃗=−3. Let θ=∠AOB.
Using the identity in part (a), find the value of sin(2θ).
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