If the lines x = -1 + s , y = 3 - s , z = 1 + s and x = t 2 , y = 1 + t , z = 2 - t with parameters s and t, are coplanar, then =

Step-by-step solution

The equations of the given lines can be written in symmetric form as: Line 1: x - (-1) 1 = y - 3 - = z - 1 = s This line passes through the point A(-1, 3, 1) and has direction ratios b₁ = 1, - , . Line 2: x - 0 1 2 = y - 1 1 = z - 2 -1 = t This line passes through the point B(0, 1, 2) and has direction ratios b₂ = 1 2 , 1, -1 . The vector joining the points A and B is: AB = (0 - (-1)) i + (1 - 3) j + (2 - 1) k = i - 2 j + k For the two lines to be coplanar, the vectors AB , b₁ , and b₂ must be coplanar. Thus, their