Question

Two unit vectors are inclined at an angle of 120°. The magnitude of their resultant is:
a)1
b)2
c)3
d)Root 3

Answer 1

Given:

Two unit vectors are inclined at an angle of 120°.

To find:

Magnitude of resultant ?

Calculation:

• Unit vector means that the magnitude of the vectors will be 1.

• Let the resultant vector be c.

$| \vec{c}| = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \theta) }$

$\implies | \vec{c}| = \sqrt{ {1}^{2} + {1}^{2} + 2.1.1 \cos( {120}^{ \circ} ) }$

$\implies | \vec{c}| = \sqrt{1+ 1 + 2 \cos( {120}^{ \circ} ) }$

$\implies | \vec{c}| = \sqrt{1+ 1 + 2 ( - \dfrac{1}{2}) }$

$\implies | \vec{c}| = \sqrt{1+ 1 - 1}$

$\implies | \vec{c}| = \sqrt{1}$

$\implies | \vec{c}| =1 \: unit$

So, resultant value is 1 unit.