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 (- → p + → q + → r ), ( → p - → q + → r

Correct answer: 0 This question is seem to be wrong but may be taken as → S = x(- → p + → q + → r ) + y( → p - → q + → r ) + z(- → p - → q + → r ) - x + y - z = 4 ..... (i) x - y - z = 3 ...... (ii) x + y + z = 5 ..... (iii) Add (i) and (ii) - 2z = 7 ⇒ z = - (7)/(2) 2x = 8 ⇒ x = 4 2x + y + z = 2(4) + 1 = 9

JEE Advanced 2015Paper 2

Exam: JEE Advanced
Year: 2015
Paper: Paper 2
Subject: Mathematics
Chapter: Vector Algebra

JEE Advanced 2015 · Paper 2 · Mathematics · Vector Algebra

Suppose that → p , → q and → r are three non - coplanar vectors in...

Suppose that

\overset{\to}{p}, \overset{\to}{q}and\overset{\to}{r}

are three non - coplanar vectors in

{\mathbb{R}}^{3}

. Let the components of a vector

\overset{\to}{s}

along

p, q

and

r

be 4,3 and 5 respectively. If the components of \left(- \overset{\to}{p} + \overset{\to}{q} + \overset{\to}{r}\right), \left(\overset{\to}{p} - \overset{\to}{q} + \overset{\to}{r}\right)and\left(- \overset{\to}{p} - \overset{\to}{q} + \overset{\to}{r}\right) are x, y and z, respectively, then the value of

2x + y + z

Correct answer

Step-by-step solution

This question is seem to be wrong but may be taken as

\overset{\to}{S} = x\left(- \overset{\to}{p} + \overset{\to}{q} + \overset{\to}{r}\right) + y\left(\overset{\to}{p} - \overset{\to}{q} + \overset{\to}{r}\right) + z\left(- \overset{\to}{p} - \overset{\to}{q} + \overset{\to}{r}\right)

- x + y - z = 4

..... (i)

x - y - z = 3

...... (ii)

x + y + z = 5

..... (iii)
Add (i) and (ii)

- 2z = 7 ⇒ z = - \dfrac{7}{2}

2x = 8 ⇒ x = 4

2x + y + z = 2\left(4\right) + 1 = 9

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