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<p>An oblique pyramid has a plane base \(ABCD\) in the shape of a parallelogram. The coordinates of \(A\), \(B\) and \(C\) are \((5,-4,1)\), \((5,4,0)\) and \((-5,4,2)\) respectively. The apex of the pyramid is at \(E(0,0,10)\) (see diagram).</p>
<ol class="i-list"><li data-list-item-id="imported-item-block-2-item-0" data-list-item-path="imported-item-block-2-item-0"><div class="list-item-paragraph">Find the coordinates of \(D\).<span class="inline-marks">[1]</span></div></li><li data-list-item-id="imported-item-block-2-item-1" data-list-item-path="imported-item-block-2-item-1"><div class="list-item-paragraph">Find the cartesian equation of face \(BCE\).<span class="inline-marks">[3]</span></div></li><li data-list-item-id="imported-item-block-2-item-2" data-list-item-path="imported-item-block-2-item-2"><div class="list-item-paragraph">Find the angle between face \(BCE\) and the base of the pyramid.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="imported-item-block-2-item-3" data-list-item-path="imported-item-block-2-item-3"><div class="list-item-paragraph">Find the shortest distance from the midpoint of edge \(AD\) to face \(BCE\).<span class="inline-marks">[5]</span></div></li></ol>

An oblique pyramid has a plane base \(ABCD\) in the shape of a parallelogram. The coordinates of \(A\), \(B\) and \(C\) are \((5,-4,1)\), \((5,4,0)\) and \((-5,4,2)\) respectively. The apex of the pyramid is at \(E(0,0,10)\) (see diagram).

Find the cartesian equation of face \(BCE\).

Find the angle between face \(BCE\) and the base of the pyramid.

Find the shortest distance from the midpoint of edge \(AD\) to face \(BCE\).