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 lines whose vector equations are : vec(r) = (hati + 2 hatj + 3 hatk ) + lambda (hati -3 hatj + 2 hatk) and vec(r) = 4 hati + 5 hatj + 6 hatk + mu (2 hati + 3 hatj + hatk) .

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 shortest distance between the following pair of line: vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(2hati+3hatj+6hatk) .

Find the shortest distance between the following pair of line: vecr=hati+2hatj+3hatk+lamda(hati-3hatj+2hatk) and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by vecr=3hati+8hatj+3hatk+lamda(3hati-hatj+hatk) and vecr=-3hati-7hatj+6hatk+mu(-3hati+2hatj+4hatk)

Find the shortest distance between the following pair of line: vecr=hati+2hatj+hatk+lamda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)

Find the shortest distance between the lines vecr = 3 hati + 2hatj - 4 hatk + lamda ( hati +2 hatj +2 hatk ) and vecr = 5 hati - 2hatj + mu ( 3hati + 2hatj + 6 hatk) If the lines intersect find their point of intersection