`ax+bx-by-cy+cx-ay`

Factorise ax + bx - ay - by

The three straight lines ax+by=c, bx+cy=a and cx +ay =b are collinear, if

The three striaght lines ax+by=c, bx+cy=a and cx+ay=b are collinear if:

The lines ax+by+c=0, bx+cy+a =0, cx+ay+b =0 are concurrent when-

The condition that the three different lines ax+by+c=0, bx+cy+a=0, cx+ay+b=0 to be concurrent is

Let a,b,c be real numbers with a^2 + b^2 + c^2 =1. Show that the equation |[ax-by-c,bx+ay,cx+a],[bx+ay,-ax+by-c,cy+b],[cx+a,cy+b,-ax-by+c]|=0 represents a straight line.

Let a,b,c be real numbers with a^2 + b^2 + c^2 =1 . Show that the equation |[ax-by-c,bx+ay,cx+a],[bx+ay,-ax+by-c,cy+b],[cx+a,cy+b,-ax-by+c]|=0 represents a straight line.

Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],[cx+az,ay+bz,cz-ax-by]| = (a^2+b^2+c^2)(ax+by+cz)(x^2+y^2+z^2)

If a,b,c are the sides of Delta ABC and the lines ax+by+c=0, bx+cy+a=0, cx+ay+b=0 are concurrent, then Delta ABC is

If ay - bx/c = cx - az/b = bz - cy/a, then prove that x/a = y/b = z/c.