Let α¯=(λ-2)a→+b→ and β¯=(4λ-2)a→+3b→ be two given vectors where vectors a→ and b¯ are non-collinear. The value of λ for which vectors a→ and β→are collinear, is

Let $\bar{α} = (λ - 2) \vec{a} + \vec{b}$ and $\bar{β} = (4 λ - 2) \vec{a} + 3 \vec{b}$ be two
given vectors where vectors $\vec{a}$ and $\bar{b}$ are non-
collinear. The value of $λ$ for which vectors $\vec{a}$ and $\vec{β}$
are collinear, is

A
$- 4$
B
3
C
$- 3$
D
4

Solution:

The given vectors are $\vec{α} = (λ - 2) \vec{a} + \vec{b}$ and

$\vec{β} = (4 λ - 2) \vec{a} + 3 \vec{b}$

Since, $\vec{α}$ and $\vec{β}$ are collinear.

$∴ \frac{λ - 2}{4 λ - 2} = \frac{1}{3} \Rightarrow 3 λ - 6 = 4 λ - 2 \Rightarrow λ = - 4$

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