Let $\rm \vec{a}, \vec{b}$ and $\rm\vec{c}$ be unit vectors such that $\rm\vec{a} \times \vec{b}$ is perpendicular to $\vec{c}$. If θ is the angle between $\rm\vec{a}$ and $\rm\vec{b}$, then which of the following is/are correct?

1. $\rm\vec{a} \times \vec{b} = sin ~\theta~ \vec{c} $

2. $\rm\vec {a} \cdot (\vec{b}\times \vec{c})=0$

Select the correct answer using the code given below.

If $\rm\vec{a}+3\vec{b} = 3\hat{i}- \hat{j}$ and $\rm2\vec{a}+\vec{b} = \hat{i}- 2\hat{j}$, then what is the angle between $\rm\vec{a}$ and $\rm\vec{b}$

If $\rm(\vec {a} + \vec{b})$ is perpendicular to $\rm\vec {a}$ and magnitude of $\rm\vec {b}$ is twice that of $\rm\vec {a}$, then what is the value of $\rm(4\vec {a} + \vec{b})\cdot \vec{b}$ equal to?

Let $\rm\vec {a}, \vec{b}$ and $ \rm \vec {c}$ be three vectors such that  $\rm\vec {a}, \vec{b}$ and $ \rm \vec {c}$  are co-planar. Which of the following is/are correct?

1. $\rm(\vec{a}\times \vec{b})\times \vec{c}$ is co-planar with $\rm\vec {a}$ and $\rm\vec {b}$

2. $\rm(\vec{a}\times \vec{b})\times \vec{c}$ is perpendicular to $\rm\vec {a}$ and $\rm\vec {b}$

Select the correct answer using the code given below.