Find the condition if lines `x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d '` are perpendicular.

The two lines x=ay+b,z=cy+d and x=a'y+b', z=c'y +d' are pendicular to each other if

Line x/a+y/b=1 cuts the coordinate axes at A(a ,0)a n dB(0,b) and the line x/a^(prime)+y/b^(prime)=-1 at A (-a ,) and B^(prime)(0,-b^(prime))dot If the points A ,B ,A^(prime),B ' are concyclic, then the orthocentre of triangle A B A ' is (0,0) (b) (0,b^(prime)) (0,(a a^(prime))/b) (d) (0,(b b^(prime))/a)

The two lines ax+by=c and a'x+b'y=c' are perpendicular if

The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity e meets the axes of the ellipse at Qa n dRdot Then the locus of the midpoint of Q R is a conic with eccentricity e ' such that (a) e^(prime) is independent of e (b) e^(prime)=1 (c) e^(prime)=e (d) e^(prime)=1/e

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

Show that the equation of the plane through the line x/l=y/m=z/n and perpendicular to the plane containing non perpendicular lines x/m=y/n=z/l and x/n=y/l=z/m is (m-n)x+(-l)y+(l-m)z=0 .

Factorise the following expressions : a x^2 y + b x y^2 + c x y z

Find the equation of the plane through the line of intersection of the planes: x+3y-z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0

Find the angle between the lines: x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+5z .