Interactive picture of a line in three dimensions together with a second line that meets it, runs parallel to it or is skew to it, or a plane with its normal vector; the parameters on each line can be changed

Not parallel still doesn't mean they meet

On a flat page, two lines that are not parallel have to cross. In space they usually miss, passing above or below each other, and only one exact pair of parameters can ever close the gap. Move λ₁ and λ₂ until the gap between the two points reaches zero, then switch to the plane and find the single λ₁ where line 1 pierces it.