The equation of the perpendicular line from the point (2,-3,1) to the line x + 1 2 = y - 3 3 = z + 2 -1 is

Step-by-step solution

Let the given point be P(2, -3, 1) and the given line be L: x + 1 2 = y - 3 3 = z + 2 -1 = . Any point on the line L can be written as Q(2 - 1, 3 + 3, - - 2) . Let Q be the foot of the perpendicular from P to the line L . The direction ratios of the line segment PQ are given by the difference of the coordinates of Q and P : a = 2 - 1 - 2 = 2 - 3 b = 3 + 3 - (-3) = 3 + 6 c = - - 2 - 1 = - - 3 Since PQ is perpendicular to the line L , the dot product of their direction ratios must be zero. The direction ratios of L a