If the straight lines x-2 1 = y-3 1 = z-4 -t and x-1 t = y-4 2 = z-5 1 are intersecting then t can have

Step-by-step solution

The given lines are L₁: x-2 1 = y-3 1 = z-4 -t = and L₂: x-1 t = y-4 2 = z-5 1 = . The general points on the lines are P₁ = (2+ , 3+ , 4-t ) and P₂ = (1+t , 4+2 , 5+ ) . For the lines to intersect, there must exist and such that P₁ = P₂ . This gives the system of equations: 1) 2+ = 1+t - t = -1 2) 3+ = 4+2 - 2 = 1 3) 4-t = 5+ t + = -1 Subtracting equation (2) from (1): (-t+2) = -2 = -2 2-t = 2 t-2 . Substituting into (2): = 1 + 2 = 1 + 4 t-2 = t+2 t-2 . Substituting and into (3): t ( t+2 t-2 ) + 2 t-2 = -1 . t^2 +