In `R_(3) , ` consider the planes `P_(1):y=0and P_(2) : x+z=1. Let P_(3)` be a plane , different from `P_(1) and P_(2)` , which passes through the interesection of `P_(1) and P_(2) `I fhte distance of the (0,1,0) from `p_(3)` is 1 and the distance of a point `(alpha , beta , gamma )` from `P_(3)` is 2, then which of the following relations is ( are ) true ?

In R^(3) , consider the planes P_(1):y=0 and P_(2),x+z=1. Let P_(3) be a plane, different from P_(1) and P_(2) which passes through the intersection of P_(1) and P_(2) , If the distance of the point (0,1,0) from P_(3) is 1 and the distance of a point (alpha,beta,gamma) from P_(3) is 2, then which of the following relation(s) is/are true?

In R^(3) , consider the planes P_(1):y=0 and P_(2),x+z=1. Let P_(3) be a plane, different from P_(1) and P_(2) which passes through the intersection of P_(1) and P_(2) , If the distance of the point (0,1,0) from P_(3) is 1 and the distance of a point (alpha,beta,gamma) from P_(3) is 2, then which of the following relation(s) is/are true? (a) 2alpha + beta + 2gamma +2 = 0 (b) 2alpha -beta + 2gamma +4=0 (c) 2alpha + beta - 2gamma- 10 =0 (d) 2alpha- beta+ 2gamma-8=0

Let two planes p _(1): 2x -y + z =2 and p _(2) : x + 2y - z=3 are given : equation of the plane through the intersection of p _(1) and p_(2) and the point (3,2,1) is :

Find the locus of P If the distance of P from (3,0) is twice the distance of P from (-3,0)

Let P_(1):x +y+2z-4=0 and P_(2): 2x-y+3z+5=0 be the planes. Let A(1, 3, 4) and B(3, 2, 7) be two points in space. The equation of a third plane P_(3) through the line of intersection of P_(1) and P_(2) and parallel to AB is

Let P_(1):x+y+2z=3 and P_(2):x-2y+z=4 be two planes. Let A(2, 4 5) and B(4, 3, 8) be two points in space. The equation of plane P_(3) through the line of intersection of P_(1) and P_(2) such that the length of the projection upon it of the line segment AB is the least, is

Let P_(1):x-2y+3z=5 and P_(2):2x-3y+z+4=0 be two planes. The equation of the plane perpendicular to the line of intersection of P_(1)=0 and P_(2)=0 and passing through (1,1,1) is

Let P_(1)=x+y+z+1=0, P_(2)=x-y+2z+1=0,P_(3)=3x+y+4z+7=0 be three planes. Find the distance of line of intersection of planes P_(1)=0 and P_(2) =0 from the plane P_(3) =0.

Let P_(1) : 2x + y + z + 1 = 0 P_(2) : 2x - y + z + 3 = 0 and P_(3) : 2x + 3y + z + 5 = 0 be three planes, then the distance of the line of intersection of planes P_(1) = 0 and P_(2) = 0 from the plane P_(3) = 0 is

Let P be a plane passing through the points (2,1,0) (4,1,1) and (5,0,1) and R be any point (2,1,6) . Then the image of R in the plane P is :