Two unit vectors are inclined at an angle, so that their resultant is also a unit vector. the angle is -

Concept:

For two vectors \(\rm \vec A\) and \(\rm \vec B\), the resultant will be:

\(\rm \left|\vec A+\vec B\right|^2=\left|\vec A\right|^2+\left|\vec B\right|^2 + 2\left(\vec A.\vec B\right)\;\)

Calculation:

Given:

\(|\vec A|=|\vec B|=1=|\vec A + \vec B|\)

\(\rm \left|\vec A+\vec B\right|^2=\left|\vec A\right|^2+\left|\vec B\right|^2 + 2\left(\vec A.\vec B\right)\;\)

\(1=1+1 + 2|\vec A|.|\vec B|\cos θ\;\)

\(1=1+1 + (2\times 1 \times 1)\cos θ\;\)

cos θ = -1/2

\(\therefore \theta =\frac{2 \pi}{3}=120^{\circ}\)