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 -p→+ q→+ r→, p→- q→+ r→ and - p→- q→+ r→ are x, y and z, respectively, then the value of 2x+y+z is

JEE Advanced · Mathematics · 30. Vector Algebra

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

Verified Solution

Answer & Solution

Correct Answer

(A) 9

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From JEE Advanced

Explore more questions on app

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 -p→+ q→+ r→, p→- q→+ r→ and - p→- q→+ r→ are x, y and z, respectively, then the value of 2x+y+z is

Step-by-step Solution