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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.
mathsVector AlgebraVector Cross Product

### Cross Product with Direction removed

In this page, you will learn about removing the direction of the vector cross product with an example application.

click on the content to continue..

An object by position vector vec p is at a distance from a screen. The screen is given by unit vector vec s Is the distance of the object from the screen a vector or scalar?

• a vector
• a vector
• a scalar

The answer is 'a vector'. The distance is a vector that terminates at the object and at 90^@ angle to the screen.

Note: In physics - Kinematics, distance and displacement are defined as scalar and vector. In coordinate geometry, distance from an object to another is a vector.

Given vec p and the screen hat s. what is the magnitude of distance of object from the screen?

• |vec p xx hat s|
• |p| sin theta
• both the above
• both the above

The answer is 'Both the above'.

An object by position vector vec p is at a distance from a screen. The screen is given by unit vector vec s We saw that the distance is a vector and the length of the distance is |vec p xx hat s|. What is the direction of the distance vector?

• unit vector along vec p - (vec p cdot hat s) hat s
• unit vector along vec p - (vec p cdot hat s) hat s
• Direction cannot be found

The answer is 'unit vector along vec p - (vec p cdot hat s) hat s'.

Vector cross product, by definition, is a vector. Depending on the application requirement, the direction can be removed.

Distance using Cross Product: For a vector vec p and a direction given by unit vector hat s, the magnitude of distance of point given by vec p to the direction hat s is |vec p xx hat s|.

slide-show version coming soon