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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 Dot Product

Dot product with Added Direction

In this page, learn about adding direction to the scalar product with an example.



click on the content to continue..

An object by position vector `vec p` casts a shadow on a screen. The screen in given by unit vector `vec s`vector dot product shadow example Is the shadow a vector or scalar?

  • a vector
  • a vector
  • a scalar

The answer is 'a vector'. The shadow is a vector that spans as a ray with a starting and end point.

`vec p` and the screen `hat s` are given.vector dot product shadow example what is the length of the shadow?

  • `vec p cdot hat s`
  • length is a scalar `|p| cos theta`
  • both the above
  • both the above

The answer is 'Both the above'.

An object by position vector `vec p` casts a shadow on a screen. The screen in given by unit vector `vec s`. We saw that the shadow is a vector and the length of the shadow is `vec p cdot hat s`.vector dot product shadow example Is the shadow as a vector?

  • `(vec p cdot hat s) hat s`
  • `(vec p cdot hat s) hat s`
  • `(vec p cdot hat s) hat p`
  • `(vec p cdot hat s) vec p`

The answer is '`(vec p cdot hat s) hat s`'.

Vector dot product by definition is a scalar. Depending on the application requirement, a direction can be added to the scalar.

Projection vector using Dot Product: For a vector `vec p` and a direction given by unit vector `hat s`, the projection vector of `vec p` in direction `hat s` is `(vec p cdot hat s) hat s`.

                            
slide-show version coming soon