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 Cross Product

### Understanding Properties of Cross Product

click on the content to continue..

Given the following
vec p = p_x i+p_yj+p_zk

vec q = q_x i+q_yj+q_zk

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

Where p_x, p_y, p_z, q_x, q_y, q_z in RR
What is the result vec p xx vec q?

• a scalar
• a vector
• a vector

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

What are the x, y, z components of the result?

• numerical expressions of real numbers
• numerical expressions of real numbers
• not numerical expressions as the terms are not numbers

The answer is 'numerical expressions of real numbers'

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

What is |p||q|sin theta?

• a numerical expression of real numbers
• a numerical expression of real numbers
• not a numerical expression as the terms are not numbers

The answer is 'a numerical expression of real numbers'

Cross product is a vector with numerical expression as components.

Cross Product as Numerical Expressions: vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|
where p_x, p_y, p_z, q_x, q_y, q_z in RR
vec p xx vec q = |p||q|sin theta
where |p|, |q|, sin theta in RR
The cross product is a numerical expression of real numbers.

To understand properties of cross product, the following are to be learned

•  Closure Law

•  Commutative Law

•  Associative Law

•  Distributive Law

•  Modulus in cross product

In learning these, which of the following would help?

• Memorize each of the laws
• use the properties of real numbers to understand the cross product as numerical expression
• use the properties of real numbers to understand the cross product as numerical expression

The answer is 'use the properties of real numbers to understand the cross product as numerical expression'.

Properties of cross product are understood from properties of real numbers applied to the numerical expression representing the cross product.

Properties of Cross Product: vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|  is considered as numerical expressions and properties of real numbers are applied to understand properties of cross product.

Solved Exercise Problem:

To understand properties of cross product, which of the following number system is used?

• Integers
• Rational numbers
• Real Numbers
• Real Numbers
• None of the above