The lines 6 x-6 18 = y+1 3 = z-1 5 and 3 x+6 12 = y-1 3 = z+1 2 are

Step-by-step solution

To analyze the relationship between the lines, their symmetric equations are rewritten and compared. The first line simplifies to x-1 3 = y+1 3 = z-1 5 , passing through P₁(1, -1, 1) with direction vector d₁ = (3, 3, 5) . The second line simplifies to x+2 4 = y-1 3 = z+1 2 , passing through P₂(-2, 1, -1) with direction vector d₂ = (4, 3, 2) . Parallelism Check: Since 3 4 3 3 5 2 , the direction vectors are not proportional; the lines are not parallel. Intersection Check: Parameterize Line 1 as x = 3 + 1 , y = 3 - 1