Show that the lines `bar (r) = ( hati + hatj - hatk) + lamda ( 3hati - hatj )` and ` bar(r) = ( 4hati - hatk ) + mu (2hati + 3hatk)` intersect. Find their point of intersection .

Show that the lines : vec(r) = 3 hati + 2 hatj - 4 hatk + lambda (hati + 2 hatj + 2 hatk) and vec(r) = 5 hati - 2 hatj + mu (3 hati + 2 hatj + 6 hatk) (ii) vec(r) = (hati + hatj - hatk) + lambda (3 hati - hatj) . and vec(r) = (4 hati - hatk) + mu (2 hati + 3 hatk) are intersecting. Hence, find their point of intersection.

Show that the lines: vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk) are intersecting. Hence find their point of intersection.

Show that the lines vecr= hati+hatj-hatk+lambda(3hati-hatj) and vecr = 4 hati+hatk+mu(2hati+3hatk) intersect. Also find the co[-ordinates of their point of intersection.

The angle between the lines bar(r) = (2hati - 5hatj + hatk) + lamda(3hati + 2hatj + 6 hatk ) "and" bar(r) = (7hati - 6hatk) + mu(hati + 2hatj + 2hatk) is

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

Show that the lines vec r = hati + hatj + t(hati - hatj +3hatk) and vecr = 2hati + hatj -hatk + s(hati + 2hatj -hatk) intersect . Find the point of intersection.

Find whether the lines vec r=(hati-hatj-hatk)+lambda(2hati+hatj) and vecr=(2hati-hatj)+mu(hati+hatj-hatk) intersect or not. If intersecting find their point of intersection.

Find whether the lines: vecr=(hati-hatj-hatk)+lambda(2hati+hatj) and vecr=(2hati-hatj)+mu (hati+hatj-hatk) intersect or not. If itersecting, find their point of intersection..

Find the angle between the lines vecr = (2hati - hatj +3hatk) + lambda(hati + hatj + 2hatk) and vec r = (hati - 3hatj)+mu(2hatj - hatk)

The acute angle between the line bar r = ( hati + 2 hatj + hatk ) + lamda (hati + hatj +hatk) and the plane bar r ( 2hati - hatj +hatk)=5