Let vec{alpha} = (lambda - 2) vec{a} + vec{b} | vedclass

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(A) Given vectors are $\vec{\alpha} = (\lambda - 2)\vec{a} + \vec{b}$ and $\vec{\beta} = (4\lambda - 2)\vec{a} + 3\vec{b}$.Since $\vec{a}$ and $\vec{b

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$-4$

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(A) Given vectors are $\vec{\alpha} = (\lambda - 2)\vec{a} + \vec{b}$ and $\vec{\beta} = (4\lambda - 2)\vec{a} + 3\vec{b}$.Since $\vec{a}$ and $\vec{b}$ are non-collinear,$\vec{\alpha}$ and $\vec{\beta}$ are collinear if and only if the ratio of the coefficients of $\vec{a}$ and $\vec{b}$ are equal.This implies $\frac{\lambda - 2}{4\lambda - 2} = \frac{1}{3}$.Cross-multiplying,we get $3(\lambda - 2) = 1(4\lambda - 2)$.$3\lambda - 6 = 4\lambda - 2$.Rearranging the terms,$3\lambda - 4\lambda = -2 + 6$.$-\lambda = 4$.Therefore,$\lambda = -4$.

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

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