Question

what will be the resultant between two equal vectors having an angle 60 degree between them

Answer 1

a\sqrt{3}

Answer 2

Let the two equal vectors be $\vec{A}$ and $\vec{B}$.
Given that the vectors are equal, their magnitudes are the same. Let this magnitude be $a$.
$|\vec{A}| = |\vec{B}| = a$.
The angle between the two vectors is given as $\theta = 60^\circ$.
The magnitude of the resultant vector $\vec{R} = \vec{A} + \vec{B}$ is given by the formula:
$|\vec{R}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}|\cos\theta}$
Substitute the given values into the formula:
$|\vec{R}| = \sqrt{a^2 + a^2 + 2(a)(a)\cos(60^\circ)}$
$|\vec{R}| = \sqrt{2a^2 + 2a^2 \cos(60^\circ)}$
We know that the value of $\cos(60^\circ)$ is $\frac{1}{2}$.
Substitute this value into the equation:
$|\vec{R}| = \sqrt{2a^2 + 2a^2 \left(\frac{1}{2}\right)}$
$|\vec{R}| = \sqrt{2a^2 + a^2}$
$|\vec{R}| = \sqrt{3a^2}$
$|\vec{R}| = a\sqrt{3}$

Thus, the magnitude of the resultant vector is $\sqrt{3}$ times the magnitude of either individual vector.