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 another 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.

Consider the line given by `vec s` and the vector `vec p` as shown in the figure. 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'.

*slide-show version coming soon*