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-

The correct option is C λc⃗ Let a #160; + 2b #160; = tc and b #160; + 3c #160; = 5c Where t and s are scalars.On adding , we ...

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Standard XII

Mathematics

Test for Collinearity of 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 $\to a + 2 \to b + 6 \to c = ?$

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 C $λ \to c$
Let $\to a + 2 \to b = t \to c$
and $\to b + 3 \to c = 5 \to c$
Where $t$ and $s$ are scalars.
On adding , we get,
$\begin{matrix} \to a + 2 \to b + 3 \to c = t \to c + s \to a \Rightarrow \to a + 2 \to b + 6 \to c = t \to c + s \to a - \to b + 3 \to c \Rightarrow t \to c + (\to b + 3 \to c) - \to b + 3 \to c = (t + 6) \to c [s \to a = \to b + 3 \to c] \Rightarrow λ \to c \end{matrix}$
Where $λ = t + 6$
Hence,
Option $C$ is correct answer.

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