Find the values of p so that the lines `(1-x)/3=(7y-14)/(2p)=(z-3)/2`and `(7-7x)/(3p)=(y-5)/1=(6-z)/5`are at right angles.

Find the values of p so that the lines (1-x)/(3)=(7y-14)/(2p)=(z-3)/(2)(7-7x)/(3p)=(y-5)/(1)=(6-z)/(5) are at right angles.

Find the values p so that line (1-x)/(3)=(7y-14)/(2p)=(z-3)/(2) and (7-7x)/(3p)=(y-5)/(1)=(6-z)/(5) are at right angles.

Fiind m, if the lines (1-x)/(3)= ( 7y-14)/(2m ) = (z-3) /(2) and ( 7-7x)/(3m) = (y-5)/(1) = (6-z)/(5) are at right angles.

Find the value of so that the lines l1: (1-x)/3 = (7y-14)/(2lambda) =(z-3)/2 and l2: (7-7x)/(3lambda) = (y-5)/1 = (6-z)/5 are at right angle. Also find the equation of a line passing through the point (3,2,-4) and parallel to l1.

Find the value of so that the lines (-(x-1))/(3)=(7(y-2))/(2lamda)=(z-3)/(2)and(-7(x-1))/(3lamda)=(y-5)/(1)=(-(z-6))/(5) are perpendicular to each other.

Find the value of p so that the lines (x+1)/(-3)=(y-p)/(2)-(z+2)/(1) and (x)/(1)=(y-7)/(1)=(z+7)/(2) are in the same plane.for this value of p,find the coordinates of their point of intersection and the equation of the plane containing them.

Find the value of p so that the lines (x+1)/(-3)=(y-p)/(2)=(z+2)/(1) and (x)/(1)=(y-7)/(1)=(z+7)/(2) are in the same plane for this value of p,find the coordinates of their point of intersection and the equation of the plane containing them.

Show that the lines (x-5)/(7) =(y+2)/(-5)=(z)/(1) " and " (x)/(1) =(y)/(2)=(z)/(3) are at right angles .

(i) Find the value of 'p' so that the lines : l_(1) : (1 - x)/(3) = (7y -14)/(2p) = (z - 3)/(2) and l_(2) : (7 -7x)/(3p) = (y - 5)/(1) = (6 - z)/(5) are at right angles. Also, find the equations of the line passing through (3,2, -4) and parallel to line l_(1) . (ii) Find 'k' so that the lines : (x - 3)/(2) = (y + 1)/(3 ) = (z - 2)/(2k) and (x + 2)/(1) = (4 -y)/(k) = (z + 5)/(1) are perpendicular to each other.

Find the value of 'lambda' so the lines: (1-x)/(3) = (7y -14)/(lambda) = (z-3)/(2) and (7 - 7x)/(3 lambda) = (y -5)/(1 ) = (6 - z)/(5) are at right angles. Also, find whether the lines are ntersecting or not .