The angle between the lines 2 x=3 y=-z and 6 x=-y=-4 z is

Step-by-step solution

The given equations of the lines are 2x = 3y = -z and 6x = -y = -4z . Rewrite the first line in standard symmetric form x a₁ = y b₁ = z c₁ . Dividing by the least common multiple of the coefficients (which is 6), we get x 3 = y 2 = z -6 . Thus, the direction vector of the first line is v₁ = 3 i + 2 j - 6 k . Rewrite the second line in standard symmetric form x a₂ = y b₂ = z c₂ . Dividing by the least common multiple of the coefficients (which is 12), we get x 2 = y -12 = z -3 . Thus, the direction vector of the sec