If the x-coordinate of a point on the join of `P(2,2,1)a n dQ(5,1,-2)i s4,` then find its `z-` coordinate.

Explanation

Suppose P divides QR in the ratio `lamda:1`
Then the coordinates of P are
`" "(5lamda+2)/(lamda+1), (lamda+2)/(lamda+1) and (-2lamda+1)/(lamda+1)`.
It is given that the x-coordinate of P is 4. Therefore,
`" "(5lamda+2)/(lamda+1)=4 or lamda=2`
So z-coordinate of P is `(-2lamda+1)/(lamda+1)=(-4+1)/(2+1)=-1`