" Sxample "16" If "(ay-bx)/(p)=(cx-az)/(q)=(bz-cy)/(r)," prove that "(x)/(a)=(y)/(b)=(z)/(c)

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

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) .

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)

(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))

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 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 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 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)|