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Question

If $\to a$ and $\to b$ are non-collinear vectors, the value of $x$ for which vectors $\to α = (x - 2) \to a + \to b$ and $\to β = (3 + 2 x) \to a - 2 \to b$ are collinear.

A

- \frac{1}{4}

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B

\frac{1}{4}

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C

1

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D

- 1

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Solution

The correct option is B $\frac{1}{4}$
Since vectors $\to α$ and $\to β$ are collinear.
Therefore, the ratio of their respective components will be same.
$\Rightarrow \frac{(x - 2)}{(3 + 2 x)} = \frac{1}{- 2} \Rightarrow 4 x - 1 = 0 \Rightarrow x = \frac{1}{4}$

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