| Date | November 2016 | Marks available | 3 | Reference code | 16N.1.hl.TZ0.4 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Hence | Question number | 4 | Adapted from | N/A |
Question
Consider the vectors a \( = \) i \( - {\text{ }}3\)j \( - {\text{ }}2\)k, b \( = - {\text{ }}3\)j \( + {\text{ }}2\)k.
Find a \( \times \) b.
Hence find the Cartesian equation of the plane containing the vectors a and b, and passing through the point \((1,{\text{ }}0,{\text{ }} - 1)\).
Markscheme
a \( \times \) b \( = - 12\)i \( - {\text{ }}2\)j \( - {\text{ }}3\)k (M1)A1
[2 marks]
METHOD 1
\( - 12x - 2y - 3z = d\) M1
\( - 12 \times 1 - 2 \times 0 - 3( - 1) = d\) (M1)
\( \Rightarrow d = - 9\) A1
\( - 12x - 2y - 3z = - 9{\text{ }}({\text{or }}12x + 2y + 3z = 9)\)
METHOD 2
\(\left( {\begin{array}{*{20}{c}} x \\ y \\ z \end{array}} \right) \bullet \left( {\begin{array}{*{20}{c}} { - 12} \\ { - 2} \\ { - 3} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 1 \\ 0 \\ { - 1} \end{array}} \right) \bullet \left( {\begin{array}{*{20}{c}} { - 12} \\ { - 2} \\ { - 3} \end{array}} \right)\) M1A1
\( - 12x - 2y - 3z = - 9{\text{ }}({\text{or }}12x + 2y + 3z = 9)\) A1
[3 marks]
