Question

three vector each of value 'a' are acting at a point such that angle between any two vectors is 120° the magnitude of their resultant is?​

Answer 1

Let's consider 3 vectors x , y , z each having magnitude a and at an angle of 120° to each other .

Refer to the attached diagram .

Let's consider vector x and y

Resultant of the 2 vectors will be :

$| \vec r| = \sqrt{ {a}^{2} + {a}^{2} + 2 {a}^{2} \cos(120 \degree) }$

$= > | \vec r| = \sqrt{ {a}^{2} + {a}^{2} + 2 {a}^{2} \times ( - \frac{1}{2}) }$

$= > | \vec r| = \sqrt{ {a}^{2} + {a}^{2} - {a}^{2} }$

$= > | \vec r| = \sqrt{ {a}^{2} }$

$= > | \vec r| = a$

So, resultant of vector x and y will be "a" units and directed opposite to vector z .

Final resultant will be :

$= | \vec z| - | \vec r|$

$= a - a$

$= 0 \: units$