(i) Find the equation of the plane passing through the points $( 2,1,0 ) , ( 5,0,1 )$ and $( 4,1,1 )$ (ii) If P is the point $( 2,1,6 )$ then the point Q such that PQ is perpendicular to the plane in (i) and the mid point of PQ lies on it.
The volume of the parallelopiped formed by vectors $\hat { i } + a \hat { j } + \hat { k } , \hat { j } + a \hat { k }$ and $a \hat { i } + \hat { k } , a > 0$ is minimum when the value of $a$ is
(i) Find the equation of the plane passing through the points $( 2,1,0 ) , ( 5,0,1 )$ and $( 4,1,1 )$
(ii) If P is the point $( 2,1,6 )$ then the point Q such that PQ is perpendicular to the plane in (i) and the mid point of PQ lies on it.