Question

Given that A$+$B$+$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 the vectors are given by.

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

Answer 1

The correct option is D ${90}^o,{135}^o,{135}^o$

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, i.e., the triangle should be right angled triangle.
Angle between A and B, $\alpha ={90}^o$
Angle between B and C, $\beta ={135}^o$
Angle between A and C, $\gamma ={135}^o$.