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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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