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 pari of lines given by (x -1)/(2) = (y -2)/(3) = (z -3)/(4) and (x -3)/(4) = (y -2)/(3) = (z -1)/(2).

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 ?

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.

Find the value of m for which the lines 4x -3y - 1 = 0, 3x - 4y + 1 = 0 and mx - 7y + 3 = 0 are concurrent.

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

For what value of p,y = x + p touches the ellipse 2x ^2 + 3y ^2 = 1 ?

Mention the condition under which the lines ( x - x _(1))/( l _(1)) = ( y - y _(1))/( m _(1)) = ( z - z _(1))/( n _(1)) and ( x - x _(2))/( l _(2)) = ( y-y _(2))/( m _(2)) = ( z - z _(2))/( n _(2)) will be perpendicular to each other.

Find the distance of the point (6, 2, -5) from the plane 2x + 3y - 2z = 8.