Test for Collinearity of Vectors

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

1. $-3$
2. $3$
3. $4$
4. $-4$

Q. Three vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are such that $\overrightarrow{a}\times \overrightarrow{b}=4(\overrightarrow{a}\times \overrightarrow{c})$ and $|\overrightarrow{a}|=|\overrightarrow{b}|=1$ and $|\overrightarrow{c}|=\frac{1}{4}$. If the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi }{3}$, then $\overrightarrow{b}$ is

1. $\overrightarrow{a}+4\overrightarrow{c}$
2. $\overrightarrow{a}-4\overrightarrow{c}$
3. $4\overrightarrow{c}-\overrightarrow{a}$
4. $2\overrightarrow{c}-\overrightarrow{a}$