QJEEAdv15Ma72bd: JEE Advanced 2015 Physics - Class 11 JEEAdv15Ma72bd Solution: Suppose that and are three non-coplanar vectors in . Let the…

Here, $\overrightarrow s = 4\overrightarrow p + 3\overrightarrow q + 5\overrightarrow r$ ....... (i)

and $\overrightarrow s = ( - \overrightarrow p + \overrightarrow q + \overrightarrow r )x + (\overrightarrow p - \overrightarrow q + \overrightarrow r )y + ( - \overrightarrow p - \overrightarrow q + \overrightarrow r )z$ ...... (ii)

$\therefore$ $4\overrightarrow p + 3\overrightarrow q + 5\overrightarrow r = \overrightarrow p ( - x + y - z) + \overrightarrow q (x - y - z) + \overrightarrow r (x + y + z)$

On comparing both sides, we get

$- x + y - z = 4$ , $x - y - z = 3$ and $x + y + z = 5$

On solving above equations, we get

$x = 4$ , $y = {9 \over 2}$ , $z = {{ - 7} \over 2}$

$\therefore$ $2x + y + z = 8 + {9 \over 2} - {7 \over 2} = 9$