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

Find the vector equation of the following plane in scalar product form : vec r=(hati+hatj)+lambda(hati+2hatj-hatk)+mu(-hati+hatj-2hatk)

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 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 vector equation of the following planes in non-parametric from: (i) vecr=( lambda -2 mu) hati+(3- mu) hatj+(2 lambda +mu) hat k (ii) vecr=(2 hati+2 hatj- hatk)+ lambda ( hati+2 hatj+3 hatk)+mu(5 hati -2 hatj +7 hatk)

Find the angle between the lines vecr = (2hati - hatj +3hatk) + lambda(hati + hatj + 2hatk) and vec r = (hati - 3hatj)+mu(2hatj - hatk)

Determine whether the following pair of lines intersect or not. i. vecr=hati-hatj+lamda(2hati+hatk), vecr=2hati-hatj+mu(hati+hatj-hatk)

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 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