Question

# Choose the correct answer Let a and b be two unit vectors and θ is the angle between them. Then, a + b is a unit vector, if a) θ=π4 b) θ=π3 c) θ=π2 d) θ=2π3

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Solution

## Let a and b be two unit vectors and θ be the angle between them. Then, |a|=|b|=1 Now, (a + b) is a unit vector if |a+b|=1⇒(a+b)2=1⇒(a+b).(a+b)=1⇒a.a+a.b+b.a+b.b=1 ⇒|a|2+|b|2+2a.b=1 [∵a.b=b.a] ⇒12+12+2a.b=1⇒a.b=−12⇒|a||b|cos θ=−12 ⇒1×1×cos θ=−12⇒cos θ=−12⇒θ=2π3

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