The value of xy - yx yz- zy zx- xz1x2- 1y2 1y2- 1z2 1z2- 1x2 is

Step-1Let xy - yx yz- zy zx- xz1x2- 1y2 1y2- 1z2 1z2- 1x2 = AB … (1)⇒ A = xy - yx yz- zy zx- xz and B = 1x2- 1y2 1y2- 1z2 1z2- 1x2 Solve the value of A and B separately.Step-2Solve for A⇒ A = xy - yx yz- zy zx- xz ⇒ A = x2- y2xy y2- z2zy z2- x2xz⇒ A = x2- y2 y2- z2 z2- x2x2 y2 z2 Step-3Now solve for BB = 1x2- 1y2 1y2- 1z2 1z2- 1x2 ⇒ B = y2- x2x2y2 z2- y2 y2z2 x2- z2z2x2 ⇒ B = y2- x2 z2- y2 x2- z2x4 y4 z4Step- 4Now from the step-2 and step-3 substitute the value of A and B in (1)We get the whole expression as⇒ AB = x2- y2 y2- z2 z2- x2x2 y2 z2 y2- x2 z2- y2 x2- z2 x4 y4 z4⇒AB = x2- y2 y2- z2 z2- x2x2 y2 z2 y2- x2 z2- y2 x2- z2x2 y2 z2(x2 y2 z2) ⇒ AB = x2- y2 y2- z2 z2- x2x2 y2 z2 x2- y2 y2- z2 z2- x2x2 y2 z2(x2 y2 z2)⇒ AB = 11-1x2 y2 z2⇒ AB = 1-1x2 y2 z2 ∴ 11 = 1 …(2)Rule of division for dividing rational expressions: abcd = ab × cdBy using above mentioned rule, (2)becomes⇒ AB = − (x2 y2 z2)⇒ AB = − x2 y2 z2Hence the value of xy - yx yz- zy zx- xz1x2- 1y2 1y2- 1z2 1z2- 1x2 is − x2 y2 z2Hence, Option(1) is the correct answer.

The value of xy - yx yz- zy zx- xz1x2- 1y2 1y2- 1z2 1z2- 1x2 is

Step-1Let xy - yx yz- zy zx- xz1x2- 1y2 1y2- 1z2 1z2- 1x2 = AB … (1)⇒ A = xy - yx yz- zy zx- xz and B = 1x2- 1y2 1y2- 1z2 1z2- 1x2 Solve the value of A and B separately.Step-2Solve for A⇒ A = xy - yx yz- zy zx- xz ⇒ A = x2- y2xy y2- z2zy z2- x2xz⇒ A = x2- y2 y2- z2 z2- x2x2 y2 z2 Step-3Now solve for BB = 1x2- 1y2 1y2- 1z2 1z2- 1x2 ⇒ B = y2- x2x2y2 z2- y2 y2z2 x2- z2z2x2 ⇒ B = y2- x2 z2- y2 x2- z2x4 y4 z4Step- 4Now from the step-2 and step-3 substitute the value of A and B in (1)We get the whole expression as⇒ AB = x2- y2 y2- z2 z2- x2x2 y2 z2 y2- x2 z2- y2 x2- z2 x4 y4 z4⇒AB = x2- y2 y2- z2 z2- x2x2 y2 z2 y2- x2 z2- y2 x2- z2x2 y2 z2(x2 y2 z2) ⇒ AB = x2- y2 y2- z2 z2- x2x2 y2 z2 x2- y2 y2- z2 z2- x2x2 y2 z2(x2 y2 z2)⇒ AB = 11-1x2 y2 z2⇒ AB = 1-1x2 y2 z2 ∴ 11 = 1 …(2)Rule of division for dividing rational expressions: abcd = ab × cdBy using above mentioned rule, (2)becomes⇒ AB = − (x2 y2 z2)⇒ AB = − x2 y2 z2Hence the value of xy - yx yz- zy zx- xz1x2- 1y2 1y2- 1z2 1z2- 1x2 is − x2 y2 z2Hence, Option(1) is the correct answer.