Question

If the two vectors are of equal in magnitude
and the same in direction at a point, then the
magnitude of resultant vector is
a)
times the magnitude of a vector
2
b) equal to the magnitude of individual
vector
c) twice the magnitude of individual vector
d) square of the magnitude of individual
vector​

Answer 1

Given :

Two vectors are of equal magnitude act in the same direction at a point.

To Find :

Magnitude of resultant vector.

Solution :

❖ As per parallelogram law of vector addition, magnitude of resultant vector R of two vectors A and B at an angle of θ is given by

$\dag\:\underline{\boxed{\bf{\orange{R=\sqrt{A^2+B^2+2AB\:cos\theta}}}}}$

In this case angle between two vectors is 0°.

Let magnitude of each vector be x.

By substituting the given values;

$\sf:\implies\:R=\sqrt{x^2+x^2+2(x)(x)\:cos0^{\circ}}$

$\sf:\implies\:R=\sqrt{2x^2+2x^2(1)}$

$\sf:\implies\:R=\sqrt{4x^2}$

$:\implies\:\underline{\boxed{\bf{\gray{R=2x}}}}$

∴ Magnitude of the resultant vector is twice the magnitude of individual vector.