Suppose that \( \vec{p}, \vec{q} \) and \( \vec{r} \) are three non...

Suppose that \( \vec{p}, \vec{q} \) and \( \vec{r} \) are three non-coplanar vectors in \( R^{3} \). Let the components of a vector \( \vec{s} \) along \( \vec{p}, \vec{q} \) and \( \vec{r} \) be 4,3 and 5 respectively. If the components of this vector \( \vec{s} \) along
\( \mathrm{P} \) \( (-\overrightarrow{\mathrm{p}}+\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{r}}),(\overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{r}}) \) and \( (-\overrightarrow{\mathrm{p}},-\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{r}}) \) are \( \mathrm{x}, \mathrm{y} \) and \( \mathrm{z} \) respectively, then the value of \( 2 \mathrm{x}+\mathrm{y}+\mathrm{z} \) is

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