Question

Two vectors each of magnitude 'a' produce a resultant vector of magnitude 'a'. Find the angle between the two original vectors.
1. \(\dfrac{\pi}{6}\)
2. \(\dfrac{\pi}{3}\)
3. \(\dfrac{2\pi}{3}\)
4. \(\dfrac{\pi}{2}\)

Answer 1

Correct Answer - Option 3 : \(\dfrac{2\pi}{3}\)

CONCEPT:

The Resultant of two vectors is given by:

R2 = (A2 + B2 + 2AB cosθ) 

where R is the resultant vector, A and B are the two vectors, and θ is the angle between two vectors.​

CALCULATION:

Given that A = B = a and R = a

We know that 

R = √(A2 + B2 + 2AB cosϕ) 

\(a=√{a^2+a^2+2a\times acosϕ}\)

\(a^2={2a^2+2a^2cosϕ}\)

\(\frac{-1}{2}={cos{ϕ}}\)

φ = \(\dfrac{2\pi}{3}\)

So the correct answer is option 3.