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Thought-Process to Discover Knowledge

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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.

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mathsVector AlgebraProperties of Cross Product

### Cross 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 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'.

slide-show version coming soon