बिंदु (1,2,-4) से गुजरने वाले तथा रेखाओं vecr =hati +2hatj -4hatk +lambda (2hati +3hatj +6hatk ...

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

Find the vector and Cartesian equations of the plane passing through the point (1,2,-4) and parallel to the lines vecr=(hati+2hatj+hatk)-lambda(2hati+3hatj+6hatk) and vecr=(hati-3hatj+5hatk)+mu(hati+hatj-hatk) .

The shortest distance between the lines vecr = (2hati - hatj) + lambda(2hati + hatj - 3hatk) vecr = (hati - hatj + 2hatk) + lambda(2hati + hatj - 5hatk)

Find the angle between the line vecr = (hati +2hatj -hatk ) +lambda (hati - hatj +hatk) and vecr cdot (2hati - hatj +hatk) = 4.

Find the points of intersection of the line vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

If vecF=2hati+3hatj-hatk and vecr=hati-hatj+6hatk find vecrxxvecF

The symmetric form of the line given by vecr =(2hati -hatj + 3hatk) + lambda(3hati - 4hatj + 5hatk) is

Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)