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 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=4hati=hatj+lamda(hati=2hatj-2hatk) and vecr=hati-hatj+2hatk-mu(2hati+3hatj-4hatk)

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

The angle between the straight line r=(2-3t)hati+(1+2t)hatj+(2+6t)hatkand r=1(1+4s)hati+(2-s)hatj+(8s-1)hatk

Find the angles between the planes vecr(hati-2hatj-2hatk)=1 and vecr(3hati-6hatj+2hatk)=0

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)

Find the angle between the planes vecr.(hati+hatj-2hatk)=3 and vecr.(2hati-2hatj+hatk)=2

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

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