Suppose that p → , q → a n d r → are three non - coplanar vectors in R 3 . Let the components of a vector s → along p , q and r be 4,3 and 5 respectively. If the components of - p → + q → + r → , p →

Question

Suppose that p → , q → a n d r → are three non - coplanar vectors in R 3 . Let the components of a vector s → along p , q and r be 4,3 and 5 respectively. If the components of - p → + q → + r → , p → - q → + r → a n d - p → - q → + r → are x, y and z, respectively, then the value of 2 x + y + z is

TestHub · Accepted Answer

This question is seem to be wrong but may be taken as
$\vec{S} = x (- \vec{p} + \vec{q} + \vec{r}) + y (\vec{p} - \vec{q} + \vec{r}) + z (- \vec{p} - \vec{q} + \vec{r})$
$- x + y - z = 4$ ..... (i)
$x - y - z = 3$ ...... (ii)
$x + y + z = 5$ ..... (iii)
Add (i) and (ii)
$- 2 z = 7 \Rightarrow z = - \frac{7}{2}$
$2 x = 8 \Rightarrow x = 4$
$2 x + y + z = 2 (4) + 1 = 9$

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