Given that `vec(A)+vec(B)+vec(C )=vec(0)`. Out of three vectors, two are equal in magnitude and the magnitude of the third vectors is `sqrt(2)` times that of either of the two having equal magnitude. Find the angles between the vectors.

Options

A. `30^(@),60^(@),90^(@)`
B. `45^(@),45^(@),90^(@)`
C. `45^(@),60^(@),90^(@)`
D. `90^(@), 135^(@),135^(@)`

Answer

D

Explanation

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, `alph= 90^(@)`
Angle between B and C, `beta= 135^(@)`
Angle between A and C, `gamma= 135^(@)`