__maths__>__Properties of Vector Arithmetics__>__Properties of Cross Product__### Cross Product of Collinear Vectors

In this page, you will learn about the vector cross 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 cross product as

`vec p xx vec q = |vec p||vec q|sin theta hat n`

What is `vec p xx vec q`, if the given vectors are collinear?

- `|p||q|sin 0 hat n`
- `|p||q|sin 180 hat n`
- `0`
- `0`
- all the above

The answer is 'all the above'. The angle between Collinear vectors can be either `0^@` or `180^@`. And `sin0 = sin180 = 0`.

Given two non-zero vectors `vec p, vec q in bbb V` have `vec p xx vec q = 0`, then what is the angle between the vectors?

- `0^@`
- `0^@`
- `90^@`
- `270^@`
- Any one of the above

The answer is '`0^@`'. It can either be `0^@` or `180^@`.

• Cross product of parallel vectors is 0 or null vector.

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

`vec p xx vec q =0 `

**Angle between vectors when cross product is `0`:** For any pair of non-zero vectors `vec p, vec q in bbb V`, If `vec p xx vec q = 0` then the vectors are collinear. The angle between them is `0^@` or `180^@`.

*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 xx vec p`?

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

The answer is '`0`'.

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