Let -2a-b and -4-2a-3b be two given vectors where vectors a and b are non-collinear- The value of - for which vectors - and - are collinear- is-

Α=(λ 2)a+b β=(4λ 2)a+3b As per question, α and β are collinear ∴ (λ 2) amp;1 (4λ 2) amp;3 =0 ⇒ 3λ 6 4λ+2=0 ⇒λ= 4 ...

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Byju's Answer

Standard XIII

Mathematics

Test for Collinearity of Vectors

Let α=λ-2a+b ...

Question

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

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Solution

The correct option is D $- 4$
$\to α = (λ - 2) \to a + \to b$
$\to β = (4 λ - 2) \to a + 3 \to b$
As per question, $\to α$ and $\to β$ are collinear
$∴ ∣ ∣ ∣ \begin{matrix} (λ - 2) & 1 (4 λ - 2) & 3 \end{matrix} ∣ ∣ ∣ = 0$
$\Rightarrow 3 λ - 6 - 4 λ + 2 = 0$
$\Rightarrow λ = - 4$

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Let →α=(λ−2)→a+→b and →β=(4λ−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:

The correct option is D −4→α=(λ−2)→a+→b →β=(4λ−2)→a+3→b As per question, →α and →β are collinear ∴∣∣∣(λ−2)1(4λ−2)3∣∣∣=0 ⇒3λ−6−4λ+2=0 ⇒λ=−4

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