<p>In the diagram, \(WXYZ\) is a trapezium and \(WX\) is parallel to \(ZY\). The point \(P\) on \(XZ\) is such that&nbsp;\(ZP:ZX=1:4\) and \(4WX=3ZY\). \(\vec{WX}=12\mathbf{p}\) and \(\vec{WZ}=4\mathbf{q}\).</p>
<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/1768032374574-3w1yvxc5hk9.png" style="max-width: min(300px, 100%); height: auto; display: block;" alt="Trapezium WXYZ with vectors p and q" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find in terms of \(\mathbf{p}\) and/or \(\mathbf{q}\),</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\(\vec{ZX}\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\vec{WP}\).</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Show that the line \(XY\) is parallel to the line \(WP\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the value of</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\(\frac{\text{area of } \Delta WPX}{\text{area of } \Delta XYZ}\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\frac{\text{area of } \Delta WZP}{\text{area of } \Delta XYZ}\).</span></div></li></ol></li></ol>

In the diagram, \(WXYZ\) is a trapezium and \(WX\) is parallel to \(ZY\). The point \(P\) on \(XZ\) is such that \(ZP:ZX=1:4\) and \(4WX=3ZY\). \(\vec{WX}=12\mathbf{p}\) and \(\vec{WZ}=4\mathbf{q}\).

Find in terms of \(\mathbf{p}\) and/or \(\mathbf{q}\),

Show that the line \(XY\) is parallel to the line \(WP\).

\(\frac{\text{area of } \Delta WPX}{\text{area of } \Delta XYZ}\),

\(\frac{\text{area of } \Delta WZP}{\text{area of } \Delta XYZ}\).

Applying Vectors to Geometric Proofs and Ratio Theory

Applying Vectors to Geometric Proofs and Ratio Theory

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