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Consider the three vectors \( \mathbf{p}, \mathbf{q} \) and \( \mathbf{r} \) such that
\( \mathbf{p}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} \) and \( \mathbf{q}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}} ; \mathbf{p} \times \mathbf{r}=\mathbf{q}+c \mathbf{p} \) and \( \mathbf{p} \cdot \mathbf{r}=2 \)
\( \mathrm{P} \)
If \( y \) is a vector satisfying \( (1+c) \mathbf{y}=\mathrm{p} \times(\mathrm{q} \times \mathrm{r}) \), then the
W vectors \( \mathbf{x}, \mathbf{y} \) and \( \mathbf{r} \)
(a) are collinear
(b) are coplanar
(c) represent the coterminus edges of a tetrahedron whose volume is \( \mathrm{c} \) cu units
(d) represent the coterminus edge of a paralloepiped whose volume is \( c \) cu units
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