The coordinates of the point of intersection of the lines x-3 1 = y-5 2 = z-1 -1 and x-4 2 = y-2 -1 = z-4 2 are...

Step-by-step solution

Let the given lines be L₁: x-3 1 = y-5 2 = z-1 -1 = and L₂: x-4 2 = y-2 -1 = z-4 2 = . Any point on L₁ is given by ( + 3, 2 + 5, - + 1) . Any point on L₂ is given by (2 + 4, - + 2, 2 + 4) . At the point of intersection, the coordinates must be equal: + 3 = 2 + 4 - 2 = 1 2 + 5 = - + 2 2 + = -3 - + 1 = 2 + 4 + 2 = -3 Solving the first and third equations: ( - 2 ) + ( + 2 ) = 1 - 3 2 = -2 = -1 Substituting = -1 in the first equation: -1 - 2 = 1 2 = -2 = -1 These values satisfy the second equation 2(-1) + (-1) = -3 . S