Question 9:
--- 9(a) ---
9(a) | Use a correct method to find OD | M1 | ( )
E.g. OC+3 OA−OB =
(–3i – 2j + 2k) + 3((2i + j – 3k) – (4j + k))
( )
AB=−2i+3j+4k
Accept column vectors throughout.
Obtain position vector of D is 3i – 11j – 10k | A1 | Accept coordinates.
2
--- 9(b) ---
9(b) | Carry out correct method for finding a vector equation for AC or BD | *M1 | E.g. 2i + j – 3k + λ (5i + 3j – 5k)
or 4j + k + µ (3i – 15j – 11k).
Condone missing r = …
Both diagonal equations correct. | A1ft | Seen or implied.
Follow their D. Condone missing r = …
Equate at least two pairs of corresponding components and solve for λ or for µ | DM1 | Dependent on using relevant lines and two
different parameters.
1 1
Obtain λ = – or µ =
4 4 | A1 | The values will depend on the directions of their
lines
3 1 7
Obtain position vector of P is i + j – k
4 4 4 | A1 | OE
Accept coordinates.
Do not ISW.
Question | Answer | Marks | Guidance
9(b) | Alternative Method for Question 9(b):
State or imply AC=5i−3j+5k | B1 FT | Or BD=3i−15j−11k
Follow their D if used.
Identify similar triangles with ratio 1 : 3 | M1
1
Use similar triangles to obtain OP, e.g. OP=OA+ AC
4 | M1 | Must be correct fraction.
3 1 7
Obtain position vector of P is i + j – k
4 4 4 | A2 | OE
Allow A1A0 if any two values are correct.
5
--- 9(c) ---
9(c) | Find direction vector BA = 2i – 3j – 4k and BC = –3i – 6j + k or equivalent | B1FT | Or ABand CB.
FT if using an incorrect AB from earlier work.
Carry out correct process for evaluating the scalar product of two relevant vectors | M1 | Allow if one is going in the negative direction,
e.g. ABand BC.
Using the correct process for the moduli, divide their scalar product by the product
of their moduli and evaluate the inverse cosine of the result to obtain an angle | M1 | Independent of the first M1.
For their two vectors
8
=cos−1 =...
29 46
Obtain answer 77.3° (or 1.35 radians) | A1 | 77.347…
Correctly rounded to more than 3 sf or
AWRT 77.3.
4
Question | Answer | Marks | Guidance