Find the vector equation of the following planes in cartesian form :
`" "vecr=hati-hatj+lamda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)`.

Explanation

The equation of the plane is `vecr=hati-hatj+lamda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)`.
Let `" "vecr=xhati+yhatj+zhatk`
Hence, the equation is `(xhati+yhatj+zhatk)-(hati-hatj)=lamda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)`
Thus, vectors `(xhati+yhatj+zhatk)-(hati-hatj), hati+hatj+hatk, hati-2hatj+3hatk` are coplanar.
Therefore, the equation of the plane is `|{:(x-1,,y-(-1),,z-0),(1,,1,,1),(1,,-1,,3):}|=0 or5x-2y-3z-7=0`