The point of intersection of the two lines x-3 3 = y-3 -1 , z - 1 = 0 and x-6 2 = z-1 3 , y - 2 = 0 is....

Step-by-step solution

The equations of the first line can be written as x-3 3 = y-3 -1 = t and z = 1 . Any point on the first line is of the form (3t+3, -t+3, 1) . The equations of the second line can be written as x-6 2 = z-1 3 = s and y = 2 . Any point on the second line is of the form (2s+6, 2, 3s+1) . At the point of intersection, the coordinates must be equal. Equating the y -coordinates, we get -t+3 = 2 t = 1 . Equating the z -coordinates, we get 1 = 3s+1 s = 0 . Substituting t = 1 in the coordinates of the first line, we get the