Let =( -2) a + b and = (4 -2) a + 3 b be two given vectors where … - Vidyadip

MCQ

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 and $\vec \alpha $ and $\vec \beta $ are collinear, is

✓
$-4$
B
$-3$
C
$4$
D
$3$

✓

Answer

Correct option: A.

$-4$

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

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

$\bar{\alpha}$ and $\bar{\beta}$ are collinear

$\left|\begin{array}{cc}{\lambda-2} & {1} \\ {4 \lambda-2} & {3}\end{array}\right|=0$

$3 \lambda-6-4 \lambda+2=0$

$-\lambda-4=0$

$\lambda=-4$

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