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 following (1-4) lines whose vector equations are : (i) vec(r) = (lambda - 1) hati + (lambda -1) hatj - (1 + lambda ) hatk and vec(r) = (1 - mu) hat(i) + (2 mu - 1) hatj + (mu + 2) hatk (ii) vec(r) = (1 + lambda) hati + (2 - lambda) hatj + (1 + lambda) hatk and vec(r) = 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 (1-4) lines whose vector equations are : 1. vec(r) = hati + hatj + lambda (2 hati - hatj + hatk ) and vec(r) = 2 hati + hatj - hatk + mu (3 hati - 5 hatj + 2 hatk) .

Find the shortest distance between the lines gives by vecr=(8+3lamda)hati-(9+16lamda)hatj+(10+7lamda)hatk and vecr=15hati+29hatj+5hatk+mu(3hati+8hatj-5hatk) .

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.

The Cartesian equation of the plane vecr=(1+lamda-mu)hati+(2-lamda+mu)hatj+(3-2lamda+2mu)hatk is

The shortest distance between lines barr=(lambda-1)hati+(lambda+1)hatj-(1+lambda)hatk and barr=(1-mu)hati+(2mu-1)hatj+(mu+2)hatk is