Prove that the lines `x=az+b,y=cz+d` and `x=a_1z + b_1,y=c_1z+d_1 ` are perpendicular if `aa_1+"cc"_1+1=0.`

Prove that the lines x = ay + b, z = cy + d and x = a'y + b' , z= c'y + d' are perpendicular, if a a' + c c' + 1=0

Find the equation of the plane Passing through the intersection of ax+by+cz+d=0 and a_1x+b_1y+c_1z+d_1=0 perpendicular to xy-plane.

Show that the lines (x-5)/(7) = (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)/(2) = (z)/(3) are perpendicular to each other.

Prove that the line (x+5)/3=(y+4)/1=(z-7)/-2 and x/1=(y+7)/5=(z-16)/-13 are coplanar.

Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y+4z-4 are co-planar.

What is the angle between the lines x/1 = y/-2 = z/1 and x/4 = y/1 = z/-2 .

Write the equation of the plane passing through the point (2, 3, 1) and perpendicular to the line. (x-1)/1=(y-2)/-1=(z+1)/3