Let \( A B C D \) be a parallelogram such that \( \mathbf{A B}=\mat...

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Let \( A B C D \) be a parallelogram such that \( \mathbf{A B}=\mathbf{q}, \mathbf{A D}=\mathbf{p} \) and \( \angle B A D \) be an acute angle. If \( r \) is the vector that coincides with the altitude directed from the vertex \( B \) to the side \( A D \), then \( r \) is given by
(a) \( r=3 q+\frac{3(\mathbf{p} \cdot q)}{(p \cdot p)} \mathbf{p} \)
(b) \( \mathbf{r}=-\mathbf{q}+\left(\frac{\mathbf{p} \cdot \mathbf{q}}{\mathbf{p} \cdot \mathbf{p}}\right) \mathbf{p} \)
(c) \( \mathbf{r}=\mathbf{q}-\left(\frac{\mathbf{p} \cdot \mathbf{q}}{\mathbf{p} \cdot \mathbf{p}}\right) \mathbf{p} \)
(d) \( \mathbf{r}=-3 \mathbf{q}+\frac{3(\mathbf{p} \cdot \mathbf{q})}{(\mathbf{p} \cdot \mathbf{p})} \mathbf{p} \)
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