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 two lines whose vector equations are given by: vecr=(1+lamda)hati+(2-lamda)hatj+(-1+lamda)hatk and vecr=2(1+mu)hati-(1-mu)hatj+(-1+2mu)hatk

Find the shortest distance between the two lines whose vector equations are given by: vecr=hati+2hatj+3hatk+lamda(2hati+3hatj+4hatk) and vecr=2hati+4hatj+5hatk+mu(3hati+4hatj+5hatk)

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 shortest distance between the lines l_(1)and l_(1) whose vector equations are vecr=(hati+hatj) + lambda (3hati + 4hatj - 2hatk) …(i) and vecr=(2hati+3hatj) + mu (6hati + 8hatj - 4hatk) …(ii)

Find the shortest distance between the lines l_(1) and l_(2) whose vector equations are (a) vecr =lambda (2hati+ 3hatj+ 4hatk) and vecr=(2hati+3hatj)+mu(2hati+3hatj+ 4hatk) (b) vecr =(hati-hatj)+lambda (hati+hatj+hatk) and a line which is parallel to previous line and passes through a point where line (x-1)/-1=(y-3)/9=(z-2)/6 cuts the x axis.

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 shortest distance between the following pair of line: vecr=(1-t)hati+(t-2)hatj+(3-2t)hatk and vecr=(s+1)hati+(2s-1)hatj-(2s+1)hatk.

Find the angle between the pair of line: vecr==(1-t)hati+(t-2)hatj+(3-2t)hatk and vecr=(s+1)hati+(2s-1)hatj-(2s+1)hatk

Find the angle between the planes whose vector equations are vecr.(2hati+2hatj-3hatk)=5 and vecr.(3hati-3hatj+5hatk)=3 .

Find the shortest distance between the lines vecr =lambda (2hati+ 3hatj+4hatk) and vecr=(hati-hatj)+t(2hati-3hatj+4hatk)