Two lines have equations r = (1, 3, 2) + s(2, -1, 3) and r = (2, 1, 4) + t(-1, 1, 4)

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.

1. [B1] Express general point of a line in component form, e.g. (1 + 2s, 3 – s, 2 + 3s) or (2 + t, 1 – t, 4 + 4t)
2. [M1] Equate at least two pairs of components and solve for s or for t
3. [A1] Obtain correct answer for s or for t (possible answers are –1, 6/5 for s and -3, 4/5 for t)
4. [A1] Verify that all three component equations are not satisfied
5. [A1] Show that the lines are not parallel and are thus skew
6. [M1] Carry out correct process for evaluating the scalar product of the direction vectors
7. [M1] Using the correct process for the moduli, divide the scalar product by the product of the moduli and evaluate the inverse cosine of the result
8. [A1] Obtain answer 19.1° or 0.333 radians