Question

Two vectors of equal magnitude have a result equal to either of them. Then, the angle between them will be $\dfrac{{2\pi }}{3}$ radians. The angle in degree is:
A. $30^\circ $
B. $120^\circ $
C. $60^\circ $
D. $45^\circ $

Answer 1

Hint: Pi does not equal any number of degrees, because pi is just a number without a unit. The point is that 180 degrees is equal to the pi radians. Radians are a unit of angle measurement, just as degrees are, and pi is just the number of radians that make up that angle. $\pi \;{\rm{radian}} = 180^\circ $

Complete step by step solution:
Given,
Two vectors of equal magnitude have a result equal to either of them. Then, the angle between them will be $\dfrac{{2\pi }}{3}$ radians.
We know that
$\begin{array}{c}\pi \;{\rm{radian}} = 180^\circ \\1\;{\rm{radian}} = \dfrac{{180}}{\pi }\\\dfrac{{2\pi }}{3}\;{\rm{radian}} = \dfrac{{2\pi }}{3} \times \dfrac{{180}}{\pi }\\ = 120^\circ \end{array}$

The radian is the SI unit for angle measurement and is the standard unit of angular measurement used in many mathematical areas. The length of an arc of a unit circle is numerically equal to the measurement of the angle it submits in radians; one radian is just below 57.3 degrees.
Degree (the right angle is 90 degrees) and gradient measure (the right angle is 100 degrees) has its uses. The arc length subtended by the central angle becomes the angle radian measure. This keeps all the significant numbers, like the central angle sine and cosine, on the same scale.

The correct option is B) $120^\circ $.

Note:
A radian is a measuring unit for angles mostly used in trigonometry. Students should take care when they convert angles into radians. While the total circle is 360 degrees, the complete circle is just over 6 radians. A full circle has 2π radians (approximately 6.28), an arc of a circle defines a radius.