Find the values `p` so that line `(1-x)/3=(7y-14)/(2p)=(z-3)/2a n d(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.

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.

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.

(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 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 '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 .

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 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.

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