Let `P_(1):2x+y-z=3" and "P_(2):x+2y+z=2` be two planes. Then, which of the following statement(s) is (are) TRUE?

Let the acute angle bisector of the two planes x - 2y - 2z + 1 = 0 and 2x - 3y - 6 z+ 1= 0 be the plane P. Then which of the following points lies on P ?

Let the acute angle bisector of the two planes x - 2y - 2z + 1 = 0 and 2x - 3y - 6 + 1= 0 be the plane P. Then which of the following points lies on P ?

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-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 to the line of intersection of P_(1)=0 and P_(2)= and passing through (1,1,1) is

Consider the three planes P_1 :3x +15 y +21 z=9 , P_2 :x - 3y -z=5 , and P_3 : 2x +10y +14 z =5 then , which one of the following is true ?

Let P_(1):x+y+2z-3=0 and P_(2)=x-2y+z=4 be two planes. Also, let A(1,3,4) and B(3,2,7) be two points in space. The equation of plane which passes through line of intersection of P_(1) and P_(2) upon which length of projection of the line segment AB is the least, is

Let P_(1):x+y+2z-3=0 and P_(2)=x-2y+z=4 be two planes. Also, let A(1,3,4) and B(3,2,7) be two points in space. The equation of plane which passes through line of intersection of P_(1) and P_(2) and upon which length of projection of the line segment AB is the greatest, is

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_(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