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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)=1a.a+a.b+b.a+b.b=1
|a|2+|b|2+2a.b=1 [a.b=b.a]
12+12+2a.b=1a.b=12|a||b|cos θ=12
1×1×cos θ=12cos θ=12θ=2π3


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