Find the vector equation of the plane
`vecr=(1s-t) hati+(2-s) hat j+(3-2s+2t) hatk`
in non-parametric from

Find the cartesian from of the equation of the plane vecr=(s-2t) hat i+(3-t) hatj+(2s+t)hat k

Find the unit vector perpendicular to the plane vec r.(2 hat i+ hat j+2 hat k)=5.

Find the vector equation of a plane through the point hati+ hat j+hat k and parallel to the plane vecr.(2 hat i-hatj +2 hatk)=5 .

Find the cartesian from of the equation of the foolowing planes: (i) vecr=( hat i- hatj)+s(- hati+ hat j+2 hat k)+t( hati+2 hatj+ hatk) (ii) vecr= (1+s+t) hat i+(2-s+t) hatj+(3-2s+2t) hatk

Find the vector equation of the following planes in scalar product from ( vec r. vec n =d) : (i) vecr=(2 hati- hatk)+ lambda hati+ mu( hati- 2 hatj- hatk) (ii) vecr=(1+s-t) hat i +(2-s) hatj+(3-2s+2t) hatk (iii) vecr=hati- hatj+ lambda ( hati + hatj+ hatk) + mu(4 hati-2 hatj +3 hatk)

Find the vector equation of the following plane in scalar product from vecr.= (hati - hatj) + lambda(hati + 2hatj - hatk) + mu (-hati + hatj + 2hatk) ,

Find the vector equations of the plane passing through the points 3 hati+ 4 hatj+2 hatk, 2hati-2 hatj -hatk and 7 hati+6 hatk .

Find the vector equation of the plane that contains the lines vec r=(hati+hatj)+lambda(hati+2hatj-hatk) and vec r=(hati+hatj)+mu(-hati+hatj-2hatk) .Also find the length of the perpendicular drawn from the point (2,1,4) to the plane thus obtained.

Find the shortest distance between the following the following lines whose vector equations are vec r=(1-t)hati+(t-2)hatj+(3-2t)hatk and vec r=(s-1)hati+(2s-1)hatj+(2s+1)hatk .

Find the vectore equation of the following plane in scalar product from : vecr=(hat i- hatj)+ lambda( hati+ hat k)+ mu ( hati-2 hatj+3 hatk)