In this page, you will learn about the result of vector dot product with a null vector.

*click on the content to continue..*

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 dot product as

`vec p cdot vec q = |vec p||vec q|cos theta`

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

- null vector
- null vector
- `vec p`
- `|vec p|`
- all the above

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

Given the definition of dot product as

`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`

What is `vec p cdot (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 dot product is `0`.

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

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

`vec p cdot vec 0 = 0`

*Solved Exercise Problem: *

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

- unknown
- `0`
- `0`
- `vec 0`

The answer is '`0`'.

*slide-show version coming soon*