1.18: Past-paper question 1

4PM1/2R/June/2025 — Question 1 · 4 marks

The points A\displaystyle A, B\displaystyle B, C\displaystyle C and D\displaystyle D are the vertices of a quadrilateral ABCD\displaystyle ABCD such that
AB→=3a+2bAD→=2a−5bAC→=5a−3b\overrightarrow{AB} = 3\mathbf{a} + 2\mathbf{b} \qquad \overrightarrow{AD} = 2\mathbf{a} - 5\mathbf{b} \qquad \overrightarrow{AC} = 5\mathbf{a} - 3\mathbf{b}
Show that ABCD\displaystyle ABCD is a parallelogram.
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