Find the Cartesian equations of the following planes whose vector equations are: `vecr.[(s-2t)hati+(3-t)hatj+(2s+t)hatk]=15`

Find the Cartesian equations of the following planes whose vector equations are: vecr.(hati+hatj-hatk)=2

Find the Cartesian equations of the following planes whose vector equations are: vecr.(2hati-7hatj+4hatk)+=0

Find the Cartesian equations of the following planes whose vector equations are: vecr.(3hati+3hatj-4hatk)=0

Find the Cartesian equation of the plane whose vector equation is vecr.(3hati+4hatj-2hatk)=5 .

Find the Cartesian equation of the plane whose vector equation is vecr.(3hati+5hatj-9hatk)=8 .

Find the cartesian equation of the plane whose vector equation is vecr.(3hati-5hatj+7hatk)+8=0

Find the Cartesian equation of a plane whose vector equation is vecr.(2hati+5hatj-4hatk)=3 .

Find the shortest distance between the two lines whose vector equations are given by: vecr=(3-t)hati+(4+2t)hatj+(t-2)hatk and vecr=(1+s)hati+(3s-7)hatj+(2s-2)hatk

Find the shortest distance between the following (6 -7) lines whose vector equations are : (i) vec(r) = (1 -t) hati + (t - 2) hatj + (3 - 2t) hatk and vec(r) = (s + 1) hat(i) + (2s - 1) hatj - (2s + 1) hatk (ii) vec(r) = (3 -t) hati + (4 + 2t) hatj + (t - 2) hatk and vec(r) = (1 + s) hati + (3s - 7 ) hatj + (2s -2) hatk. where t and s are scalars.

Find the Cartesian equation of the following planes : a. vec(r). (hati + hatj - hatk ) = 2 b. vec(r). (2 hati + 3 hatj - 4 hatk ) = 1 (c ) vec(r). [ (s - 2t) hati + (3 - t ) hatj + (2 s + t ) hatk] = 15