If a → = i ^ + j ^ −2 k ^ , b → =2 i ^ − j ^ + k ^ and c → =3 i ^ − k ^ . If c → =m a → +n b → then m+n=

Correct answer: (C) 2. c ¯ = m a ¯ + n b ¯ ⇒3i¯-k¯=mi¯+mj¯-2mk¯+2ni¯-nj¯+nk¯ ⇒ 3i¯-k¯=m+2ni¯+m-ni¯+n-2mk¯ ∴ m+2n=3 ...... (i) m-n=0 ...... (ii) n-2m=-1 .... (iii) As m-n=0 from (ii) ∴ m=n ∴ 3m=3 ∴ m=1 and n=1 ∴ m+n=2

Q79 / 150 · MHT CET 2016 · Mathematics

If $\vec{a} = \hat{i} + \hat{j} - 2 \hat{k}, \vec{b} = 2 \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = 3 \hat{i} - \hat{k}$ . If $\vec{c} = m \vec{a} + n \vec{b}$ then $m + n =$

A
$0$
B
$1$
Correct answer
C
$2$
D
$- 1$

Solution

\bar{c} = m \bar{a} + n \bar{b}

\Rightarrow 3 \bar{i} - \bar{k} = m \bar{i} + m \bar{j} - 2 m \bar{k} + 2 n \bar{i} - n \bar{j} + n \bar{k}

\Rightarrow 3 \bar{i} - \bar{k} = (m + 2 n) \bar{i} + (m - n) \bar{i} + (n - 2 m) \bar{k}

∴ m + 2 n = 3

...... (i)

m - n = 0

...... (ii)

n - 2 m = - 1

.... (iii)
As

m - n = 0

from (ii)

∴ m = n

∴ 3 m = 3

∴ m = 1 a n d n = 1

∴ m + n = 2

Hence, the correct answer is option: 'C'.

If a → = i ^ + j ^ −2 k ^ , b → =2 i ^ − j ^ + k ^ and c → =3 i ^ − k ^ . If c → =m a → +n b → then m+n=

Solution

Relevant Questions

If $\vec{a} = \hat{i} + \hat{j} - 2 \hat{k}, \vec{b} = 2 \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = 3 \hat{i} - \hat{k}$ . If $\vec{c} = m \vec{a} + n \vec{b}$ then $m + n =$