Consider the following statements:

1. The cross product of two unit vectors is always a unit vector.

2. The dot product of two unit vectors is always unity.

3. The magnitude of sum of two unit vectors is always greater than the magnitude of their difference.

Which of the above statements are not correct?

Concept:

The cross product of two vectors is given by  and 

The scalar product of two vectors is given by

If  is a unit vector then 

Calculations:

Statement 1: The cross product of two unit vectors is always a unit vector.

Let  and  are two unit vectors.

i.e 

As we know that, the cross product of two vectors is given by  and 

⇒ 

The range of sin θ is [-1, 1]

So, it is not necessarily true that the cross product of two unit vectors is always a unit vector.

Hence, statement 1 is false.

Statement 2: The dot product of two unit vectors is always unity.

Let  and  are two unit vectors.

i.e 

As we know that, the scalar product of two vectors is given by  

⇒ 

The range of cos θ is [-1, 1].

So, it is not necessarily true that the dot product of two unit vectors is always a unit vector.

Hence, statement 2 is false.

Statement 3: The magnitude of sum of two unit vectors is always greater than the magnitude of their difference.

Let  

As we can see that, the vectors   and  are two unit vectors

⇒   and 

⇒ 

So, statement 3 is also false.

Hence, the correct option is 4.