question_answer

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

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

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

C) \[90{}^\circ ,\text{ }135{}^\circ ,\text{ }45{}^\circ \]

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

Correct Answer: D

Solution :

[d] Angle between \[\vec{A}\] and \[\vec{B}\] is \[{{90}^{o}}\] Between \[\vec{B}\] and \[\vec{C}\] is \[135{}^\circ \] and that between \[\vec{A}\] and \[\vec{C}\] is \[135{}^\circ \].