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 ?

Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0?