A line passing through the points (1, -1, 2) and (2, 0, 1) meets the XY plane and the YZ plane at points A and B respectively. The distance AB is equal to...

Step-by-step solution

The equation of the line passing through (1, -1, 2) and (2, 0, 1) is given by: x - 1 2 - 1 = y - (-1) 0 - (-1) = z - 2 1 - 2 x - 1 1 = y + 1 1 = z - 2 -1 = Any point on this line can be written as ( + 1, - 1, - + 2) . The line meets the XY plane at point A, where the z-coordinate is zero: - + 2 = 0 = 2 Substituting = 2 , the coordinates of A are (3, 1, 0) . The line meets the YZ plane at point B, where the x-coordinate is zero: + 1 = 0 = -1 Substituting = -1 , the coordinates of B are (0, -2, 3) . The distance betw