Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsProperties of Vector ArithmeticsProperties of Dot Product

### Dot product with a null vector

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