question_answer

Given that\[\vec{A}+\vec{B}+\vec{C}=0\]. Out of three vectors two are equal in magnitude and the magnitude of third vector is 2 times that of either of the two having equal magnitude. Then the angles between vectors are given by

A) \[30{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ \]     

B) \[45{}^\circ ,\text{ }45{}^\circ ,\text{ }90{}^\circ \]

C) \[45{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ \]     

D) \[90{}^\circ ,\text{ }135{}^\circ ,\text{ }135{}^\circ \]

Correct Answer: D

Solution :

From the polygon law, three vectors having summation zero should form a closed polygon. (Triangle) since the two vectors are having same magnitude and the third vector is V2 times that of either of two having equal magnitude, i.e., the triangle should be right angled triangle Angle between A and B, \[\alpha  =90{}^\circ \] Angle between B and C, \[\beta  =135{}^\circ \] Angle between A and C, \[\gamma  =135{}^\circ \]