Question

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 $\sqrt{2}$ times that of either of the two having equal magnitude. Then the angles between vectors are given by

• A. $30^{\circ },60^{\circ },90^{\circ }$
• B. $45^{\circ },45^{\circ },90^{\circ }$
• C. $45^{\circ },60^{\circ },90^{\circ }$
• D. $90^{\circ },135^{\circ },135^{\circ }$

Answer 1

Answer: (D)

From 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 $\sqrt{2}$ times that of either of two having equal magnitude.
That is, 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 $C,\gamma =135^{\circ }$