<p>In the diagram, \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) represent vectors \(\mathbf{a}\) and \(\mathbf{b}\) respectively. \(X\), \(Y\) and \(Z\) are points such that&nbsp;\(\overrightarrow{OX} = \frac{3}{2}\overrightarrow{OB}\), \(\overrightarrow{AY} = \frac{2}{3}\overrightarrow{AB}\) and \(\overrightarrow{OZ} = \lambda\overrightarrow{OA}\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Express \(\overrightarrow{OX}\) and \(\overrightarrow{OY}\) in terms of \(\mathbf{a}\) and/or \(\mathbf{b}\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Express \(\overrightarrow{XZ}\) in terms of \(\lambda\), \(\mathbf{a}\) and \(\mathbf{b}\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given that&nbsp;\(\lambda = \frac{3}{5}\), find the ratio of \(XY : XZ\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find \(\frac{\text{area of } \Delta OYZ}{\text{area of } \Delta AYZ}\).</span></div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1768035372078-ucv5vvm15uk.png" style="max-width: min(220px, 100%); height: auto; display: block;" alt="Vector diagram with points \(O, A, B, X, Y, Z\)" class="aligncenter custom-width" /></figure></div>

In the diagram, \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) represent vectors \(\mathbf{a}\) and \(\mathbf{b}\) respectively. \(X\), \(Y\) and \(Z\) are points such that \(\overrightarrow{OX} = \frac{3}{2}\overrightarrow{OB}\), \(\overrightarrow{AY} = \frac{2}{3}\overrightarrow{AB}\) and \(\overrightarrow{OZ} = \lambda\overrightarrow{OA}\).

Express \(\overrightarrow{OX}\) and \(\overrightarrow{OY}\) in terms of \(\mathbf{a}\) and/or \(\mathbf{b}\).

Express \(\overrightarrow{XZ}\) in terms of \(\lambda\), \(\mathbf{a}\) and \(\mathbf{b}\).

Evaluating Vector Sums and Differences Numerically

Evaluating Vector Sums and Differences Numerically

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