Consider the lines `L_(1) : x/3 +y/4 = 1 , L_(2) : x/4 +y/3 =1, L_(3) : x/3 +y/4 = 2 and L_(4) : x/4 + y/3 = 2` .Find the relation between these lines.

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

Consider the lines : L_1: (x-7)/3=(y-7)/2=(z-3)/1 and L_2: (x-1)/2=(y+1)/4=(z+1)/3 . If a line 'L' whose direction ratios are intersects the lines L_1 and L_2 at A and B respectively, then the distance of (AB)/2 is:

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

Consider the line L_(1) : (x-1)/(2)=(y)/(-1)=(z+3)/(1), L_(2) : (x-4)/(1)=(y+3)/(1)=(z+3)/(2) find the angle between them.

Read the following passage and answer the questions. Consider the lines L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2) L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3) Q. The shortest distance between L_(1) and L_(2) is

Find the angle between the planes 2x-3y+4z=1 and -x+y=4 .

Read the following passage and answer the questions. Consider the lines L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2) L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3) Q. The distance of the point (1, 1, 1) from the plane passing through the point (-1, -2, -1) and whose normal is perpendicular to both the lines L_(1) and L_(2) , is

Show that the lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 are coplanar. Also find the equation of the plane containing the lines.

Show that the lines (x-1)/(2)=(y-3)/(4)=-z and (x-4)/(2)=(y-1)/(-2)=(z-1)/(1) are coplanar Also find the equation of the plane containing the lines.