## Exam-Style Question on Vectors## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 399. This question is similar to one that appeared on an A-Level paper. The use of a calculator is allowed.

The points A and B have coordinates \((3,-2,1)\) and \((4, 0, -1)\) respectively.

The line \(l\) has the following equation equation:

$$ r= \begin{pmatrix} 3 \\ 2 \\ 0 \\ \end{pmatrix} + \lambda \begin{pmatrix} -1 \\ -2 \\ 0 \\ \end{pmatrix} $$The point C lies on \(l\) where \(\lambda = 3\).

(a) Find the coordinates of C.

(b) Find the acute angle ABC, giving your answer to the nearest tenth of a degree.

(c) The point D lies on a line through A and B such that angle ADC is a right angle. Find the coordinates of D.

(d) The point E completes the parallelogram ACBE. Find the coordinates of E.

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