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

Open in App

Solution

BONUS

But the examiner may have given the question in following way,
If the vectors $\to p, \to q$ and $\to r$ are three orthogonal non-coplanar vectors in $R^{3}$ , then

$\to S = 4 \to p + 3 \to q + 5 \to r \to S = x (- \to p + \to q + \to r) + y (\to p - \to q + \to r) + z (- \to p - \to q + \to r)$
So,
$- x + y - z = 4 x - y - z = 3 x + y + z = 5 \Rightarrow x = 4 \Rightarrow z = - 3.5 \Rightarrow y = 4.5 2 x + y + z = 8 + 4.5 - 3.5 = 9$

Suggest Corrections

Similar questions

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 ___

Q. Suppose that

\to p, \to q

and

\to r

are three non-coplanar vectors in

R^{3} .

Let the components of a vector

\to s

along

\to p, \to q,

and

\to r

4, 3,

and

5,

respectively. If the components of this vector

\to s

along

(- \to p + \to q + \to r),

(\to p - \to q + \to r),

and

(- \to p - \to q + \to r),

are

x, y,

and

z,

respectively, then the value of

2 x + y + z

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 ___