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

The correct option is D 0⃗ Since, a⃗+2b⃗ is collinear with c⃗ . ∴a⃗+2b⃗=xc⃗, xϵ R and b⃗+3c⃗ is collinear with a⃗ . ∴b⃗+3c⃗ ...

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Byju's Answer

Standard IX

Mathematics

Collinear Vectors

Let a⃗, b⃗ ...

Question

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

λ \to a

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λ \to b

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λ \to c

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\to 0

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Solution

The correct option is D $\to 0$
Since, $\to a + 2 \to b$ is collinear with $\to c$ .
$∴ \to a + 2 \to b = x \to c, x ϵ R$ and $\to b + 3 \to c$ is collinear with $\to a$ .
$∴ \to b + 3 \to c = y \to a, y ϵ R$
$\Rightarrow \to a + 2 \to b + 6 \to c = (1 + 2 y) \to a$
Also, $\to a + 2 \to b + 6 \to c = (x + 6) \to c$
$∴ (x + 6) \to c = (1 + 2 y) \to a$
$\Rightarrow x + 6 = 0$
and $1 + 2 y = 0$
$\Rightarrow x = - 6$ and $y = - 1 / 2$
$∴ \to a + 2 \to b + 6 \to c = \to 0$

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