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

∵ α → , β → are collinear then, λ - 2 4 λ - 2 = 1 3 ⇒ λ = - 4 .

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MathematicsVectorGeneral definitions, Angle between vectors, Section formula, Geometrical resultsEasy2 minPYQ_2019

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

Options:

Answer:

Solution:

$∵ \vec{α}, \vec{β}$ are collinear then, $\frac{λ - 2}{4 λ - 2} = \frac{1}{3} \Rightarrow λ = - 4$ .

Stream:JEESubject:MathematicsTopic:VectorSubtopic:General definitions, Angle between vectors, Section formula, Geometrical results

⏱ 2mℹ️ Source: PYQ_2019

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