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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 AlgebraVector Dot Product

Vector Dot Product : Projection of a vector

In this page, you will learn about computing projection of vector using vector dot product.



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Vector dot product is understood as product between components in parallel to each other.
In finding the component in parallel to one vector the vector is projected on to anothervector dot product projection form in the figure, What is `a` ?

  • `a` is the projection of `vec q` onto `vec p`
  • `a` is the projection of `vec q` onto `vec p`
  • `a` is the projection of `vec p` onto `vec q`

The answer is '`a` is the projection of `vec q` onto `vec p`'

The vector dot product can be used to find projection of a vector on a line. vector dot product projection form

Consider the line given by `vec s` and the vector `vec p` as shown in the figure.vector dot product projection form We know that `vec s cdot vec p = |vec s| |vec p| cos theta`.
To find the projection of `vec p` on `vec s`, which of the following can be used?

  • `hat s cdot vec p`, where `hat s` is unit vector
  • `(vec s)/(|vec s|) cdot vec p`
  • both the above
  • both the above

The answer is 'both the above'.

Vector dot product can be used to find projection of a vector on a line or on another vector.

Projection of a vector: Projection of a vector `vec p` on a line in direction `vec s` is
`= vec p cdot hat s`
where `hat s` is the unit vector along `vec s`.

Solved Exercise Problem:

Two vectors `vec p` and `vec q` with magnitudes `2` and `3` respectively are at an angle `60^@`. What is the projection of `vec p` on `vec q`?

  • `2 xx cos 60^@`
  • `2 xx 1/2`
  • 1
  • all the above
  • all the above

The answer is 'All the above'.

                            
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