Question 10:
--- 10(i) ---
10(i) | Equate at least two pairs of components and solve for s or for t | M1 |  s= −4  s= −2
 3 s=−6  5
  t = −5 or   t =−11 or   t = −13
3 5
  
7≠−7
−5≠ −1 6 ≠ −8
 3 5 5
Obtain correct answer for s or t, e.g. s = – 6, t = – 11 | A1
Verify that all three equations are not satisfied and the lines fail
to intersect | A1
State that the lines are not parallel | B1
4
--- 10(ii) ---
10(ii) | EITHER: Use scalar product to obtain a relevant
equation in a, b and c, e.g. 2a + 3b – c = 0 | B1
Obtain a second equation, e.g. a + 2b +c = 0,
and solve for one ratio, e.g. a : b | M1
Obtain a : b : c and state correct answer, e.g.
5i – 3j + k, or equivalent | A1
OR: Attempt to calculate vector product of
relevant vectors, e.g. (2i + 3j – k)×(i + 2j + k) | M1
Obtain two correct components | A1
Obtain correct answer, e.g. 5i – 3j + k | A1
3
Question | Answer | Marks | Guidance
--- 10(iii) ---
10(iii) | EITHER: State position vector or coordinates of the
mid-point of a line segment joining points on l
3 5
and m, e.g. i+j + k
2 2 | B1 | OR: Use the result of (ii) to form equations of planes containing
l and m B1
Use the result of (ii) and the mid-point to
find d | M1 | Use average of distances to find equation of p. M1
Obtain answer 5x – 3y + z = 7, or equivalent | A1 | Obtain answer 5x – 3y + z = 7, or equivalent A1
OR: Using the result of part (ii), form an equation
in d by equating perpendicular distances to
the plane of a point on l and a point on m | M1
14−d −d
State a correct equation, e.g. =
35 35 | A1
Solve for d and obtain answer 5x – 3y + z =
7, or equivalent | A1
3