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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 vectors $\vec{a}$ and $\vec{b}$ are non-collinear. The value of $\lambda$ for which vectors $\vec{\alpha}$ and $\vec{\beta}$ are collinear, is:
Option 1)
-4
Option 2)
4
Option 3)
3
Option 4)
-3

Answers (1)

best_answer

Collinear Vectors -

Two vectors are said to be collinear if their directed line segments are parallel disregards to their direction.

- wherein

If $\vec{a}$ and $\vec{b}$ are collinear , then $\vec{a}= K\vec{b}$ where K $\epsilon$ R

Collinear Vectors -

Two vectors are said to be collinear if and only if there exists a scalar m such as that $\vec{a}=m\vec{b}$

- wherein

m is a Scalar.

Given vectors are

$\vec{\alpha }=(\lambda -2)\vec{a}+\vec{b}$

$\vec{\beta }=(4\lambda -2)\vec{a}+3\vec{b}$

As $\vec{a }\: and\: \: \vec{b}$ are non-collinear

$\frac{\lambda -2}{4\lambda -2}=\frac{1}{3}$

$\lambda=-4$

Option 1)
-4
Option 2)

4

Option 3)

3

Option 4)

-3

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