4MA0 Higher June 2013 Paper 4 Q21
21
Diagram NOT accurately drawn
\(PQRS\) and \(PSTU\) are parallelograms.
\(\overrightarrow{PU} = \mathbf{a}\quad \overrightarrow{PS} = \mathbf{b}\quad \overrightarrow{PQ} = \mathbf{c}\)
Find, in terms of \(\mathbf{a}\), \(\mathbf{b}\) and \(\mathbf{c}\)
(i) \(\overrightarrow{TQ}\)
(ii) \(\overrightarrow{PX}\) where \(X\) is the midpoint of \(TQ\).
Simplify your answer as much as possible.
Simplify your answer as much as possible.
(3)
| Scheme | Marks |
|---|---|
| (i) \(-\mathbf{a} - \mathbf{b} + \mathbf{c}\) | B1 |
| (ii) \(PX = PU + UT + \tfrac{1}{2}TQ\) oe | M1 ft |
| \(\tfrac{1}{2}(\mathbf{a} + \mathbf{b} + \mathbf{c})\) | A1 |
| (3) |
Notes
B1: any order
M1 ft: any valid route in capitals or lower case
A1: accept \(\tfrac{1}{2}\mathbf{a} + \tfrac{1}{2}\mathbf{b} + \tfrac{1}{2}\mathbf{c}\)