__maths__>__Properties of Vector Arithmetics__>__Properties of Cross Product__### Cross product with a null vector

In this page, you will learn about vector cross product with a null vector.

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What is a null vector or zero vector?

- A vector of magnitude `0`
- `0i+0j+0k`
- `vec 0`
- all the above
- all the above

The answer is 'All the above'

Given the definition of cross product as

`vec p xx vec q = |vec p||vec q|sin theta hat n`

What is `vec p xx (vec 0)`?

- null vector
- null vector
- `vec p`

The answer is 'Null Vector' As `|vec 0| = 0`, the cross product is `0`.

Given the definition of cross product as

`vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`

What is `vec p xx (vec 0)`?

- `vec 0`
- `vec 0`
- `vec p`
- `p_x+p_y+p_z`
- all the above

The answer is '`vec 0`' As all the x, y, z components of `vec 0` is `0`, the cross product is `0`.

• Cross product with a null vector results in a null vector.

** Cross product with null vector: ** For any vector `vec p in bbb V`

`vec p xx vec 0 = 0`

*Solved Exercise Problem: *

Given that `vec x` has unknown magnitude and direction. What is the result of `vec 0 xx vec x`?

- unknown
- `-vec(x)`
- `-vec(x)`
- `vec 0`

The answer is '`vec 0`'.

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