Show that line `(x-3)/2=(y+1)/-3=(z-2)/4` is perpendicular to the line `(x+2)/2=(y-4)/4=(z+5)/2`

Show that the line 4x=3y=-z is perpendicular to the line 3x=-y=-4z

Show that the lines (x-3)/(2)=(y+1)/(-3) =(z-2)/(4) " and " (x+2)/(2) =(y-2)/(4) =(z+5)/(2) are perpendicular to each other .

(i) Find the equations of the straight line passing through the point (2,3,-1) and is perpendicular to the lines : ( x-2)/(2) = (y + 1)/(1) = (z - 3)/(-3) and (x - 3)/(1) = (y + 2)/(1) = (z - 1)/(1) . (ii) Find the equation of the line which intersects the lines : (x + 2)/(1) = (y - 3)/(2) = (z + 1)/(4) and (x - 1)/(2) = (y - 2)/(3) = (z - 3)/(4) Perpendicular and passes through the point (1,1,1) .

(i) Find the vector and cartesian equation of the line passing through the point (1,2,-4) and perpendicular to the two lines : (x - 8)/(3) = (y + 19)/(-16) = (z - 10)/(7) and (x - 15)/(3) = (y - 19)/(8) = (z - 5)/(-5) . (ii) Find the vector and cartesian equations of the line passing through the point (2,1,3) and perpendicular to the lines : (x -1)/(1) = (y -2)/(2) = (z - 3)/(3) and (x)/(-3) = (y)/(2) = (z)/(5) .

Equation of the plane containing the straight line (x)/(2)=(y)/(3)=(z)/(4) and perpendicular to the plane containing the straight lines (x)/(2)=(y)/(4)=(z)/(2) and (x)/(4)=(y)/(2)=(z)/(3) is

The equation of the plane containing the straight line x/2=y/3=z/4 and perpendicular to the plane containing the straight lines x/3=y/4=z/2 and x/4 =y/2 =z/3 is :

Equation of the plane containing the straighat line x/2=y/3=z/4 and perpendicular to the lane containing the straighat lines x/3=y/4=z/2 and x/4=y/2=z/3 is (A) x+2y-2z=0 (B) 3x+2y-2z=0 (C) x-2y+z=0 (D) 5x+2y-4z=0

Equations of the line through (4,-5,6) and perpendicular to the lines (x-11)/1=(y+6)/(-3) = (z-5)/0 and (x-1)/5 = (y-2)/2=(z-8)/11 are

The line (x-3)/1=(y-4)/2=(z-5)/2 cuts the plane x+y+z=17 at

If the line (x-2)/-1=(y+2)/1=(z+k)/4 is one of the angle bisector of the lines x/1=y/-2=z/3 and x/-2=y/3=z/1 then the value of k is