<prompt> Tuseme kwamba pointi leftrho,theta,phi rightleft 12, frac2 pi3, fracpi4 kulia ndani viwianishi vya duara vinaweza kuonyeshwa kama x, y, z katika viwianishi vya mstatili. Tafuta xz.  <response>: Tuna hiyo rho 12, theta frac2 pi3, na phi fracpi4, hivyoanzaalignx rho sin phi cos theta 12 sin fracpi4 cos frac2 pi3 12 cdot frac1sqrt 2 cdot kushoto -frac12 kulia -3 sqrt2, y rho sin phi sin theta 12 sin fracpi4 sin frac2 pi3 12 cdot frac1sqrt 2 cdot fracsqrt32 3 sqrt6, z rho cos phi 12 cos fracpi4 12 cdot frac1sqrt2 6 sqrt2.endalignKwa hivyo, tuna x z 3sqrt2. 