question_answer 1)

Find the shortest distance between the lines            

Answer:

On comparing the given equations with       and       we get, x1 = ?1, y1 = ?1, z1 = ?1; a1 = 7,       b1 = ?6, c1 = 1       and x2 = 3, y2= 5, z2= 7; a1 = 1,       b2 = ?2, c2 = 1       Now       + (b1c2 ? c1b2)2 + (c1a2 ? a1c2)2       = (?14 ? (?6))2 + (?6 ? (?2))2 + (1 ? 7)2       = (?14 + 6)2 + (?6 + 2)2 + (?6)2       = 64 + 16 + 36 = 116.       Now shortest distance between the lines is given by