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June 2003 p1 q8
2225
The points A, B, C and D have position vectors \(3oldsymbol{i} + 2oldsymbol{k}\), \(2oldsymbol{i} - 2oldsymbol{j} + 5oldsymbol{k}\), \(2oldsymbol{j} + 7oldsymbol{k}\) and \(-2oldsymbol{i} + 10oldsymbol{j} + 7oldsymbol{k}\) respectively.
(i) Use a scalar product to show that \(\overrightarrow{BA}\) and \(\overrightarrow{BC}\) are perpendicular. [4]
(ii) Show that \(\overrightarrow{BC}\) and \(\overrightarrow{AD}\) are parallel and find the ratio of the length of \(BC\) to the length of \(AD\). [4]
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