Question

If resultant of two unit vectors â and ^b is also a unit vector, then magnitude of difference of â and ^b is (1) Zero (2) 1 (4) V2 (3) V3​

Answer 1

Let nˆ1 and nˆ2 are the two unit vectors,then sum is

n→s=n→1+nˆ2.

⇒n2s=n21+n22+2n1n2cosθ=1+1+2cosθ

Since it is given that n→s is a unit vector, so ns=1.

∴1=1+1+2cosθ⇒cosθ=−12⇒θ=120∘

Now the diffrence vector is n→d=n→1−n→2

⇒n2d=n21+n22−2n1n2cosθ=1+1−2cos(120∘)=3

⇒nd=3–√