SATHEE: Vectors 1 Question 31

Vectors 1 Question 31

32. Suppose that $p, q$ and $r$ 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 this vector $s$ along $(- p + q + r)$ , $(p - q + r)$ and $(- p - q + r)$ are $x, y$ and $z$ respectively, then the value of $2 x + y + z$ is

(2015 Adv.)

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Answer:

Correct Answer: 32. (9)

Solution:

Here, $s = 4 p + 3 q + 5 r$

and $s = (- p + q + r) x + (p - q + r) y + (- p - q + r) z$

$∴ 4 p + 3 q + 5 r = p (- x + y - z) + q (x - y - z) + r (x + y + z)$

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

$\begin{aligned} x & = 4, y = \frac{9}{2}, z = \frac{- 7}{2} \\ ∴ 2 x + y + z & = 8 + \frac{9}{2} - \frac{7}{2} = 9 \end{aligned}$

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Vectors 1 Question 31

32. Suppose that p,q and r are three non-coplanar vectors in R3. Let the components of a vector s along p,q and r be 4,3 and 5 , respectively. If the components of this vector s along (−p+q+r), (p−q+r) and (−p−q+r) are x,y and z respectively, then the value of 2x+y+z is

Answer:

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