If a-b-c are three non-zero vectors- no two of which are collinear- a-b is collinear with c and b-3c is collinear with a- then -a-2b-6c- will be equal to

A+2b=λc...(i) b+3c=μa,......(ii) where no two of a, b and c are collinear vectors Eliminating b from above relations, ⇒a 6 c=λc 2μa ⇒a(1+2μ) =(λ+6)c Since a, ...

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Byju's Answer

Standard XI

Mathematics

Collinear Vectors

If a,b,c are ...

Question

If $\to a, \to b, \to c$ are three non-zero vectors, no two of which are collinear, $\to a + \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ , then $| \to a + 2 \to b + 6 \to c |$ will be equal to

zero

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Solution

The correct option is A
zero

$\to a + 2 \to b = λ \to c . . . (i) \to b + 3 \to c = μ \to a, . . . . . . (i i)$
where no two of $\to a, \to b a n d \to c$ are collinear vectors
Eliminating $\to b$ from above relations,
$\Rightarrow \to a - 6 \to c = λ \to c - 2 μ \to a \Rightarrow \to a (1 + 2 μ) = (λ + 6) \to c$
Since $\to a, \to b$ are non-collinear and non-zero,
$1 + 2 μ = 0, λ + 6 = 0 \Rightarrow μ = - \frac{1}{2}, λ = - 6$

$\to a + 2 \to b = - 6 \to c \Rightarrow \to a + 2 \to b + 6 \to c = \to 0$

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If $\to a, \to b, \to c$ are three non-zero vectors, no two of which are collinear, $\to a + \to b$ is collinear with $\to c$ and $\to b + 3 \to c$ is collinear with $\to a$ , then $| \to a + 2 \to b + 6 \to c |$ will be equal to