Unanswered 3d And Vectors Questions

If the angle between a, b is twice the angle between a, c & b, c, then find the value of [a, b, c]. Here a, b, c represents unit vectors..... ...

*Image* In the soln its given that no three planes can meet at two distinct points. But we can have infinite number of planes through a given line. isnt it? Plese clarify ...

a detalied explanation for what a nilpotent matrix is...i need it... ps---NISHANT SIR, help... ...

Can anyone explain reciprocal system of vectors? Its the only topic I am not understanding properly! :/ ...

Points x and y lie on the side QR and RS of a parallelogram PQRS such that QX =2XR and RY=3YS.Thus the value of u such that the diagonal PR meets line XY at Z and PZ=u PR is ?Characters in bold face denote vectors. ...