Pairs of Lines in 3D (Edexcel A-Level Further Mathematics): Flashcards

Direction vectors are scalar multiples: $\mathbf{b}_1 = k\mathbf{b}_2$

Not parallel and do not intersect

$\mathbf{r}_1 = \mathbf{r}_2$ has a consistent solution

Three equations (one for each component)

$\lambda$ and $\mu$ simultaneously

Substitute back to find intersection point

$\mathbf{b}_1 = k\mathbf{b}_2$, $k \in \mathbb{R}$

Neither parallel nor intersecting

Three component equations

Lines may be skew (no intersection exists)