Work out collinear points instantly with clear inputs, formula shown and shareable results.
Points are collinear when the vectors between them are parallel, which makes their cross product the zero vector. Half that cross product's magnitude is the area of the triangle they form.
Collinearity test
AB × AC = 0 ⇔ A, B and C lie on one line
Triangle area
Area = ½|AB × AC|
Yes. AC = (6, 9, 12) is exactly three times AB = (2, 3, 4), so the cross product vanishes.
Gradients break down for vertical lines and do not extend cleanly to three dimensions; the cross product handles every case.