question_answer 1)

Find the equations of the lines joining the following pair of vertices and then find the shortest distance between the lines: (i) (0, 0,0), (1, 0, 2), (ii) (1, 3, 0), (0, 3, 0)  

Answer:

We know that equation of line passing through the two points (x1, y1, z1) and (x2, y2, z­2) is given by              equation of line passing through (0, 0, 0) an (1, 0, 2) is                   i.e.,       Also, equation of line passing through (1, 3, 0), and (0, 3, 0) is             i.e.       To find shortest distance between             Here x1 = 1, y1 = 0, z1 = 2; a1 = ?1, b1 = 0, c1 = ?2.       And       b2 = 0, c2 = 0                                   = (0 ? 0)2 + (0 ? 0)2 + (2 ? 0)2 = 4       Now shortest distance between the lines is given by       S.D. =