Higher November 2020 Paper 3 Q23
23 In triangle JKL
M is the midpoint of JK
JN : NL = 3 : 2
\(\overrightarrow{KL}\) = 7a \(\overrightarrow{NL}\) = 4b
Not drawn accurately
Work out \(\overrightarrow{JM}\) in terms of a and b.
Give your answer in its simplest form. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| (\(\overrightarrow{JN}\) =) \(\dfrac{3}{2} \times 4\mathbf{b}\) or \(6\mathbf{b}\) | M1 | oe eg (\(\overrightarrow{NJ}\) =) \(-6\mathbf{b}\) implied by \(\overrightarrow{JL}\) = \(10\mathbf{b}\) may be seen on diagram |
| (\(\overrightarrow{JK}\) =) their \(6\mathbf{b} + 4\mathbf{b} - 7\mathbf{a}\) or \(10\mathbf{b} - 7\mathbf{a}\) | M1dep | oe eg (\(\overrightarrow{KJ}\) =) \(7\mathbf{a} - 10\mathbf{b}\) |
| \(5\mathbf{b} - \dfrac{7}{2}\mathbf{a}\) or \(5\mathbf{b} - 3.5\mathbf{a}\) | A1 | oe eg \(\dfrac{1}{2}(10\mathbf{b} - 7\mathbf{a})\) SC2 \(3.5\mathbf{a} - 5\mathbf{b}\) or \(\dfrac{7}{2}\mathbf{a} - 5\mathbf{b}\) |