Let a¯,b¯ and c¯ are three non –zero vectors no two of which are collinear. If a¯+2b¯ is collinear with c¯ and b¯+3c¯ is collinear with a¯ then a¯+2b¯+6c¯

a¯+2b¯=tc¯ ⇒ a¯+2b¯+6c¯=(t+6)c¯……….1 and b¯+3c¯=ra¯⇒a¯+2b¯+6c¯=(2r+1)a¯……(2) From (1) \& (2) t+6=0⇒t=−6 ∴a¯+2b¯+6c¯=O¯

Let a¯,b¯ and c¯ are three non –zero vectors no two of which are collinear. If a¯+2b¯ is collinear with c¯ and b¯+3c¯ is collinear with a¯ then a¯+2b¯+6c¯

a¯+2b¯=tc¯ ⇒ a¯+2b¯+6c¯=(t+6)c¯……….1 and b¯+3c¯=ra¯⇒a¯+2b¯+6c¯=(2r+1)a¯……(2) From (1) \& (2) t+6=0⇒t=−6 ∴a¯+2b¯+6c¯=O¯

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Let $\bar{a}, \bar{b} and \bar{c}$ are three non –zero vectors no two of which are collinear. If $\bar{a} + 2 \bar{b}$ is collinear with $\bar{c} and \bar{b} + 3 \bar{c}$ is collinear with $\bar{a} then \bar{a} + 2 \bar{b} + 6 \bar{c}$

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$\bar{O}$

$λ \bar{a}$

$λ \bar{b}$

$λ \bar{c}$

answer is A.

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Detailed Solution

$\bar{a} + 2 \bar{b} = \bar{tc} \Rightarrow \bar{a} + 2 \bar{b} + 6 \bar{c} = (t + 6) \bar{c} \dots \dots \dots . (1) a n d \bar{b} + 3 \bar{c} = r \bar{a}$
$\Rightarrow \bar{a} + 2 \bar{b} + 6 \bar{c} = (2 r + 1) \bar{a} \dots \dots (2) From (1) \& (2) t + 6 = 0 \Rightarrow t = - 6 ∴ \bar{a} + 2 \bar{b} + 6 \bar{c} = \bar{O}$