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

(D) From polygon law, there 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 `90^(@)`
Angle between B and C is `135^(@)`
Angle between A and C is `135^(@)`