Question 48

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


Correct Answer: 9


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