<prompt> Pointi ina viwianishi vya mstatili 2,-1,-2 na viwianishi vya duara rho, theta, phi. Tafuta viwianishi vya mstatili vya uhakika vilivyo na viwianishi vya duara rho, theta, 2 phi.  <response>: Tuna hiyo rho sqrt22 -12 -22 3. Tunataka phi kutosheleza-2 3 cos phi,hivyo cos phi -frac23. Kwa kuwa phi ni kali,sin phi sqrt1 - cos2 phi fracsqrt53.Tunataka theta kukidhianzaalign2 3 cdot fracsqrt53 cos theta, -1 3 cdot fracsqrt53 sin theta.endalignKwa hivyo, cos theta frac2sqrt5 na sin theta -frac1sqrt5.Halafu kwa uhakika na kuratibu za duara rho, theta, 2 phi,anzaalignx rho sin 2 phi cos theta 3 2 sin phi cos phi cos theta 3 kushoto 2 cdot fracsqrt53 cdot kushoto -frac23 kulia kulia frac2sqrt5 -frac83, y rho sin 2 phi sin theta 3 2 sin phi cos phi cos theta 3 left 2 cdot fracsqrt53 cdot kushoto -frac23 kulia kulia kushoto -frac1sqrt5 kulia frac43, z rho cos 2 phi 3 cos2 phi - sin2 phi 3 kushoto frac49 - frac59 kulia -frac13.endalignKwa hivyo, viwianishi vya mstatili ni left -frac83, frac43, -frac13 kulia. 