d
(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. i.e. the triangle should be right angled triangle

Angle between \(A\) and \(B\), \(\alpha\) \(= 90°\)

Angle between \(B\) and \(C\), \(\beta\) \(= 135°\)

Angle between \(A\) and \(C\), \(\gamma\) \(= 135°\)