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Consider three planes P1 : x-y + z = 1, ...

Consider three planes `P_1 : x-y + z = 1`, `P_2 : x + y-z=-1` and `P_3 : x-3y + 3z = 2` Let `L_1, L_2` and `L_3` be the lines of intersection of the planes `P_2 and P_3`, `P_3 and P_1` and `P_1 and P_2` respectively.Statement 1: At least two of the lines `L_1, L_2 and L_3` are non-parallel . Statement 2:The three planes do not have a common point

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Consider three planes P_(1):x-y+z=1 , P_(2):x+y-z=-1 and P_(3):x-3y+3z=2 . Let L_(1),L_(2),L_(3) be the lines of intersection of the planes P_(2) and P_(3),P_(3) and P_(1),P_(1) and P_(2) respectively. Statement I Atleast two of the lines L_(1),L_(2) and L_(3) are non-parallel. Statement II The three planes do not have a common point.

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

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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 :

If L_1 is the line of intersection of the planes 2x-2y+3z-2=0 x-y+z+1=0 and L_2 is the line of the intersection of the planes x+2y-z-3=0 3x-y+2z-1=0 then the distance of the origin from the plane containing the lines L_1 and L_2 is

Let P_(1) and P_(2) be two planes containing the lines L_(2) and L_(2) respectively. STATEMENT-1 : If P_(1) and P_(2) are parallel then L_(1) and L_(2) must be parallel. and STATEMENT-2 : If P_(1) and P_(2) are parallel the L_(1) and L_(2) may not have a common point.

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.

Consider the line L 1 : x +1/3 = y+ 2/1= z +1/2 L2 : x-2/1= y+2/2= z-3/3 The unit vector perpendicular to both L 1 and L 2 lines is

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