If the vectors `xhati+hatj+hatk,hati+yhatj+hatk and hati+hatj+zhatk` are coplanar where, `x ne1,y ne1 and z ne1`, then prove that
`(1)/(1-x)+(1)/(1-y)+(1)/(1-z)=1`

Explanation

The vectors are coplanar, if we can fiind two scalars `lamda and mu` such that
`(xhati+hatj+hatk)=lamda(hati+yhatj+hatk)+mu(hati+hatj+zhatk)`
`impliesx=lamda+mu,1=lamda y+mu,1=lamda+muz`
`implies x=lamda+mu,y=(1-mu)/(lamda),z=(1-lamda)/(mu)`
`implies 1-x=1-lamda-mu,1-y=(lamda-1+mu)/(lamda)`
`1-z=(mu-1+lamda)/(mu)`
`therefore(1)/(1-x)+(1)/(1-y)+(1)/(1-z)=(1)/(1-lamda-mu)+(lamda)/(lamda+mu-1)+(mu)/(lamda+mu-1)`
`=(-1+lamda+mu)/(lamda+mu-1)=1`
`implies(1)/(1-x)+(1)/(1-y)+(1)/(1-z)=1`.