Find the cartesian form of the equation of the plane.
`vecr=(lambda-mu)hati+(1-mu)hatj+(2lambda+3mu)hatk`

Explanation

`vecr=(lambda-mu)hati+(1-mu)hatj+(2lambda+3mu)hatk`
`rArr vecr= hatj+lambda(hati+2hatk)+mu(-hati-hatj+3hatk)`
Comparing with equation `vecr = veca+lambdavecb+muvecc`
`veca = hatj, vecb=hati+2hatk` and `vecc = -hati+hatj+3hatk`
`:. vecn=vecbxxvecc=|{:(hati,hatj,hatk),(1,0,2),(-1,-1,3):}|`
`= hati(0+2)-hatj(3+2)hatk(-1-0)`
`=2hati-5hatj-hatk`
Equation of plane in scalar product form
`vecr.vecn = veca.vecn`
`rArr (xhati+yhatj+zhatk).(2hati-5hatj-hatk)`
`= hatj.(2hati-5hatj-hatk)`
`rArr 2x-5y - z = - 5`.