Using the diagram and your knowledge of vectors, show that BCD is a straight line

BC = BA - CA = (3a - b) - (a + 4b) = 2a - 5b BD = BA + AB = (3a - b) + (a - 9b) = 4a - 10b BC = 1/2 BD. Using basic vector rules, we know that if vectors are multiples, then they are parallel. Since BC and BD start at the same point, we can deduce that they are on a straight line. Points lying on a straight line are known as collinear and BC and BD are scalar multiples of each other.