Find the angle between the pari of lines given by `(x -1)/(2) = (y -2)/(3) = (z -3)/(4) and (x -3)/(4) = (y -2)/(3) = (z -1)/(2).`

Find the value 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 intersect each other are right angle.

Find the angle between the lines x-sqrt 3y=1 and sqrt 3x-y=1 .

Show that the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x+1)/(1)=(y+2)/(2)=(z+3)/(-2) are perpendicular.

If the lines (x -1)/(-3) = (y -2)/(2 lamda ) = ( z -3)/( 2) and ( x -1)/( 3 lamda ) = ( y-1)/(1) = ( z - 6)/( -5) are perpendicular to each other , what is the value of lamda ?

Find the direction cosines of the line (4-x)/(2)=(y)/(6)=(1-z)/(3) .

Find the acute angle between the lines x - sqrt3 y = 1 and sqrt3 x -y = 4

What is the angle between the planes x + y + 2z = 6 and 2x - y - z =9 ?