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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.continue
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.



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An object by position vector `vec p` is at a distance from a screen. The screen is given by unit vector `vec s`vector cross product distance example 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`.vector cross product distance example 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|`.vector cross product distance example 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