Question

Derive expression for magnitude of resultant of two concurrent vector

Answer 1

Firstly we must know that the concurrent vectors have the same origin and cross a single point, also a vectorial magnitude is that which has a number, direction and sense.

Let A and B be two concurrent vectors, the direction is expressed by COSθ then the resulting magnitude is given by the following expression:

R = √(A^2+ B^(2 )+2.A.B.COSθ)

Answer 2

concurrent vector means vectors which have same initial point as shown in figure, $\vec{A}$ and $\vec{B}$ are concurrent vector.
now Resultant of concurrent vector is given by , $\vec{R}=\vec{A}-\vec{B}$

and magnitude of resultant of A and B is given by $\bf{R}=\sqrt{A^2+B^2-2ABcos\theta}$
where $\theta$ is angle between $\vec{A}$ and $\vec{B}$.