Consider the following statements :

1. Dot product over vector addition is distributive

2. Cross product over vector addition is distributive

3. Cross product of vectors is associative

Which of the above statements is/are correct ?

Let  $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that  $\vec{a}\times \vec{b} = \vec{c} $. Consider the following statements:

1. $\vec a$ is unique if $\vec b$ and $\vec c$ are given

2. $\vec c$ is unique if $\vec a$ and $\vec b$ are given

Which of the above statements is/are correct?

Let $\vec a$ and $\vec b$ be two unit vectors such that $|\vec a - \vec b|<2.$ If 2θ is the angle between $\vec a$ and $\vec b,$ then which one of the following is correct ?

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.