Question

Find the shortest distance between the lines (x – 8)/3 = (y + 9)/(–16) = (z – 10)/7 and (x – 15)/3 = (y – 29)/8 = (z – 5)/(–5).

Find the equations of the diagonals of the parallelogram PQRS whose vertices are P(4, 2, -6), Q(5, -3, 1), R(12, 4, 5) and S(11, 9, -2). Use these equations to find the point of intersection of diagonals.

A line l passes through point (-1, 3, -2) and is perpendicular to both the lines x/1 = y/2 = z/3 and (x + 2)/-3 = (y - 1)/2 = (z + 1)/5. Find the vector equation of the line l. Hence, obtain its distance from origin.

Find the distance between the lines x = (y − 1)/2 = (z − 2)/3 and x + 1 = (y + 2)/2 = (z − 1)/3.