Determine whether the following pair of lines intersect or not.
i. `vecr=hati-hatj+lamda(2hati+hatk), vecr-2hati-hatj+mu(hati+hatj-hatk)`
ii. `vecr=hati+hatj-hatk+lamda(3hati-hatj), vecr=4hati-hatk+mu(2hati+3hatk)`

Find the shortest distance between the following lines : (i) vecr=4hati-hatj+lambda(hati+2hatj-3hatk) and vecr=hati-hatj+2hatk+mu(2hati+4hatj-5hatk) (ii) vecr=-hati+hatj-hatk+lambda(hati+hatj-hatk) and vecr=hati-hatj+2hatk+mu(-hati+2hatj+hatk) (iii) (x-1)/(-1) = (y+2)/(1) = (z-3)/(-2) and (x-1)/(1) = (y+1)/(2) = (z+1)/(-2) (iv) (x-1)/(2) = (y-2)/(3) = (z-3)/(4) and (x-2)/(3) = (y-3)/(4) = (z-5)/(5) (v) vecr = veci+2hatj+3hatk+lambda(hati-hatj+hatk) and vecr = 2hati-hatj-hatk+mu(-hati+hatj-hatk)

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

Find the angle between the following pairs of lines. (i) hatr = 2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and vecr = 7 hati-6hatk+mu(hati+2hatj+2hatk) (ii) vecr = 3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr= 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the angle between each of the following pair of line: vecr=5hati-7hatj+lamda(-hati+4hatj+2hatk) vecr=-2hati+hatk+mu(3hati+3hatk)

Find the angle between the following pair of line: vecr=3hati+hatj-2hatk+lamda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-3hatk)

The equation of the plane containing the lines vecr=(hati+hatj-hatk)+lamda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk) , is

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

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 angle between the line: vecr=4hati-hatj+lamda(hati+2hatj-2hatk) and vevr=hati-hatj+2hatk-mu(2hati+4hatj-4hatk)

Find the angle between the pair of line: vecr=3hati+2hatj-4hatk+lamda(hati+2hatj+2hatk), vecr=5hati-2hatk+mu(3hati+2hatj+6hatk)