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

# Let  $\overline{\alpha }=\left(\lambda -2\right)\stackrel{\to }{a}+\stackrel{\to }{b}$ and $\overline{\beta }=\left(4\lambda -2\right)\stackrel{\to }{a}+3\stackrel{\to }{b}$ be two given vectors where vectors $\stackrel{\to }{a}$ and $\overline{b}$ are non-collinear. The value of $\lambda$ for which vectors $\stackrel{\to }{a}$ and $\stackrel{\to }{\beta }$are collinear, is

1. A

$-4$

2. B

3

3. C

$-3$

4. D

4

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

The given vectors are $\stackrel{\to }{\alpha }=\left(\lambda -2\right)\stackrel{\to }{a}+\stackrel{\to }{b}$and

$\stackrel{\to }{\beta }=\left(4\lambda -2\right)\stackrel{\to }{a}+3\stackrel{\to }{b}$

Since, $\stackrel{\to }{\alpha }$ and $\stackrel{\to }{\beta }$are collinear.

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)