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 this vector $\vec{s}$ along - p → +   q → +   r…

Question

Suppose that p &#8594; , &#160; q &#8594; &#160; a n d &#160; r &#8594; are three non - coplanar vectors in R 3 . Let the components of a vector s &#8594; along $p, q$ and $r$ be 4,3 and 5 respectively. If the components of this vector $\vec{s}$ along - p &#8594; + &#160; q &#8594; + &#160; r &#8594; , &#160; &#160; p &#8594; - &#160; q &#8594; + &#160; r &#8594; &#160; a n d &#160; - &#160; p &#8594; - &#160; q &#8594; + &#160; r &#8594; are x, y and z, respectively, then the value of 2 x + y + z is

Aicharya · 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

Suppose that p → ,   q →   a n d   r → are three non - coplanar vectors in…

Solution

Suppose that p &#8594; , &#160; q &#8594; &#160; a n d &#160; r &#8594; are three non - coplanar vectors in…

Solution

Suppose that p → , q → a n d r → are three non - coplanar vectors in…