Find the vector equation of the following plane in product form `vecr = ( hati-hatk)+lambda(hati+2hatj)+mu(hati+3hatj-hatk)`.

Explanation

Comparing with `vecr = veca+lambdavecb+muvecc`
`veca=hati-hatk,vecb=hati+2hatj,vecc=hati+3hatj-hatk`
`vecn=vecbxxvecc=|{:(hati,hatj,hatk),(1,2,0),(1,3,-1):}|`
`=hati(-2-0)-hatj(-1-0)+hatk(3-2)`
`=-2hati+hatj+hatk`
Equation of plane
`vecr.vecn=veca.vecn`
`rArr vecr.(-2hati+hatj+hatk) = (hati-hatk).(-2hati+hatj+hatk)`
`= -2-1`
`= - 3`
`rArr vecr.(-2hati+hatj+hatk) = - 3`