1.

Let P denotes the plane consisting of all points thata are equidistant from the points A(-4,2,1) and B(2,-4,3) and Q be the plane, x-y+cz=1 where c in R. The planar P is parallel to plane Q

Answer»

for no value of c
if c=3
if c`=1//3`
if c=1

Solution :
Plane P will CONTAIN the point `M(-1,-1,2)` and dr's of its NORMAL will be proportional to `(3,-3,1)`.
Thus, equation of the plane P is
`3(x+1)-3(y+1)+1(z-)=0`
`therefore P:3x-3y+z-2=0`………..(1)
`therefore P:3x-3y+z-2=0`
Also, `Q:x-y+cz-1=0` ......(2)
If P is parallel to Q then
`3/1=1/c rArr c=1/3`.


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