[" Show that the lines "vec r=(2hat i-3hat k)+lambda(hat i+2hat j+3hat k)" and "vec r=(2hat i+6hat j+3hat k)],[+mu(2hat i+3hat j+4vec k)" intersect.Also,find their point intersection."]

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Shortest distance between the lines: vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+u(2hat i+4hat j-5hat k)

Show that the lines vec r=3hat i+2hat j-4hat k+lambda(hat i+2hat j+2hat k)vec r=5hat i-2hat j+mu(3hat i+2hat j+6hat k); are intersecting.Hence find their point of intersection.

Show that the lines vec r=(hat i+hat j-hat k)+lambda(3hat i-hat j) and vec r=(4hat i-hat k)+mu(2hat i+3hat k) are coplanar.Also,find the plane containing these two lines.

Show that the lines vec( r) =(hat(i) +hat(j) -hat(k)) +lambda (3hat(i) -hat(j)) " and " vec( r) =(4hat(i) -hat(k)) + mu (2hat(i) +3hat(k)) intersect . Find the point of the intersection.

If vec r=(hat i+2hat j+3hat k)+lambda(hat i-hat j+hat k) and vec r=(hat i+2hat j+3hat k)+mu(hat i+hat j-hat k) are bisector of two lines is

Find the shortest distance between the lines vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) are coplanar. Also, find the plane containing these two lines.

The lines vec r=(hat i+hat j+hat k)alpha+3hat k and vec r=(hat i-2hat j+hat k)beta+3hat k