__maths__>__Properties of Vector Arithmetics__>__Properties of Dot Product__### Dot product of Collinear Vectors

In this page, you will learn about the result of vector dot product between two collinear vectors.

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When two vectors are called 'collinear' vectors? `color(coral)(text(co)) + color(deepskyblue)(text(linear))` means `color(coral)(text(together))+color(deepskyblue)(text(on a line))`

- the angle between vectors `0^@`
- the angle between vectors `180^@`
- the vectors are parallel
- all the above
- all the above

The answer is 'All the above'.

Given the definition of dot product as

`vec p cdot vec q = |vec p||vec q|cos theta`

What is `vec p cdot vec q`, when the given vectors are collinear?

- `|p||q|cos 0`
- `|p||q|cos 180`
- one the above
- one the above

The answer is 'one the above'. The angle between Collinear vectors can be either `0^@` or `180^@`.

• Dot product of parallel vectors is product of the magnitudes of the vectors.

Dot product of anti-parallel vectors is negative of product of the magnitudes of the vectors.

**Dot Product of Collinear Vectors: ** For any pair of collinear vectors `vec p, vec q in bbb V`,

If they are parallel making `0^@` angle

`vec p cdot vec q =|p||q| `

If they are anti-parallel making `180^@` angle,

`vec p cdot vec q =-|p||q| `

*Solved Exercise Problem: *

Given `vec p= 2i+3.1j+.5k` and `vec q = 2i+3.1j+.5k` what is the angle between them?

- `90^@`
- `45`
- `180^@`
- `0^@`
- `0^@`

The answer is '`0^@`'. The vectors are identical.

*Solved Exercise Problem: *

Given a vector `vec p` with magnitude `12`, what is `vec p cdot vec p`?

- `12`
- `sqrt(12)`
- `12xx12`
- `12xx12`
- `12 cos 0`

The answer is '`12xx12`'.

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