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

If (bz + cy)/a = (cx +az)/b = (ay+bx)/c , then prove that x/(a(b^(2) + c^(2) - a^(2))) = y/(b(c^(2) + a^(2) - b^(2))) = z/(c(a^(2)+b^(2)-c^(2))) .

If x = cy + bz, y = az + cx , z =bx + ay, then prove that x^2/(1-a^2)= y^2/(1-b^2)

If x = cy+bz, y =az+cx, z = bx+ay then prove that x^2/(1-a^2)=y^2/(1-b^2)=z^2/(1-c^2) .

If x = cy + bz, y = az + cx,z = bx + ay where x,y,z are not all zero, prove that a^2 + b^2 + c^2 + 2ab = 1.

(bz+cy)/a=(cx+az)/b=(ay+bx)/c then prove x/(a(b^2+c^2-a^2))=y/(b(c^2+a^2-b^2))=z/(a(a^2+b^2-c^2))

Given x = cy+bz, y = az + cx, z = b x + ay where, x,y,z are not all zero prove that a^2+b^2 +c^2 + 2 a b c = 1.

Consider the system of equations ax + by + cz = 2 bx + cy + az = 2 cx + ay + bz = 2 where a,b,c are real numbers such that a + b + c = 0. Then the system

If (ax+by)/(x+y)=(bx+az)/(x+z)=(ay+bz)/(y+z) and x+y+z=!0 then show that each ratio is (a+b)/2

If A=ax+by+cz , B=bx+cy+az , C=cx+ay+bz and a+b+c=0 , then prove that A^3+B^3+C^3=3ABC