If `x + y + z = 0,` prove that `|(ax,by,cz),(cy,az,bx),(bz,cx,ay)|=xyz|(a,b,c),(c,a,b),(b,c,a)|`

If u=ax+by+cz , v=ay+bz+cx , w=az+bx+cy , then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

If u=ax+by+cz , v=ay+bz+cx , w=ax+bx+cy , then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

If u=ax+by+cz , v=ay+bz+cx , w=ax+bx+cy , then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

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

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

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) .

det[[ Prove that ax-by-cz,ay+bx,cx+azay+bx,by-cz-ax,bz+cycx+az,bz+cy,cz-ax-by]]=(x^(2)+y^(2)+z^(2))(a^(2)+b^(2)+c^(2))(ax+by+cz)

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))) .

prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),,(b-z)^(2)),((c-x)^(2),,(c-y)^(2),,(c-z)^(2)):}| |{:((1+ax)^(2),,(1+bx)^(2),,(1+cx)^(2)),((1+ay)^(2),,(1+by)^(2),,(1+cy)^(2)),((1+az)^(2),,(1+bx)^(2),,(1+cz)^(2)):}| =2 (b-c)(c-a)(a-b)xx (y-z) (z-x)(x-y)