Two unit vectors a-hat and b-hat satisfy |a-hat+b-hat|=1. Which set is correct for a-hat·b-hat, |a-hat×b-hat| and |a-hat-b-hat|?
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Question

Two unit vectors a-hat and b-hat satisfy |a-hat+b-hat|=1. Which set is correct for a-hat·b-hat, |a-hat×b-hat| and |a-hat-b-hat|?

G1 Physics · Accepted Answer

1=|a+b|²=2+2a·b, so a·b=−1/2 and θ=120°. Cross magnitude=sin120°=√3/2. Difference squared=2−2(−1/2)=3, so |a−b|=√3.