Question
If the sum of two unit vectors is a unit vector, then magnitude of difference is
Answer: Option B
:
B
Let ^n1 and ^n2 are the two unit vectors, then the sum is
⃗ns = ^n1 + ^n2 or ns2 = n12 + n22 + 2n1n2cosθ
= 1 + 1 + 2cosθ
Since it is given that ns is also a unit vector, therefore 1 = 1+ 1 + 2 cos θ = ⇒ cos θ = - 12 ∴ θ = 120∘
Now the difference vector is ^nd = ^n1 - ^n2 or n12 + n22 - 2n1n2cosθ = 1 + 1 - 2 cos(120∘)
∴ nd2 = 2 - 2(- 12) = 2 + 1 = 3 ⇒ nd = √3
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:
B
Let ^n1 and ^n2 are the two unit vectors, then the sum is
⃗ns = ^n1 + ^n2 or ns2 = n12 + n22 + 2n1n2cosθ
= 1 + 1 + 2cosθ
Since it is given that ns is also a unit vector, therefore 1 = 1+ 1 + 2 cos θ = ⇒ cos θ = - 12 ∴ θ = 120∘
Now the difference vector is ^nd = ^n1 - ^n2 or n12 + n22 - 2n1n2cosθ = 1 + 1 - 2 cos(120∘)
∴ nd2 = 2 - 2(- 12) = 2 + 1 = 3 ⇒ nd = √3
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