Question

A line in direction l is defined by the vector relation u = a + ls , where l is a unit vector and s is a scalar parameter −∞ < s < ∞. Show that this will intersect a second line v = b + ms, where m is a unit vector if

a dot ( l x m ) = b dot ( l x m) and determine the point of intersection, i.e. values of s for each line at the intersection

Answer 1

If the lines intersect then for some scalar s, the position vector of the point would be same. then we have the following:

multiplying both side the cross product of the unit vectors l and m we get

Note that

since

Hence Proved