Question

# If then the vectors and

- Are mutually Perpendicular
- Coplanar
- Forms a Parallelopiped of volume 2 units
- Forms a Parallelopiped of volume 3 units

Hint:

### We have three vectors. Two of the vectors are based on the other two given vectors. We have to find the relation between the vectors.

## The correct answer is: Are mutually Perpendicular

### The vectors are given as follows:

Let the other three vectors be denoted as

We have to find the relation between the vectors.

Now, we will first find the components of the vectors

So, the vectors become.

Now, we will take their dot product to check if they are mutually perpendicular or not.

So, the given vectors are perpendicular.

If we see all the vectors are perpendicular to each other.

The given vectors are mutually perpendicular.

We can check for parallelepiped. We can take the scalar product of the given vectors. If we do that, we will find the volume to be 6 units. It doesn't match any option.

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