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

In this page, you will learn about the vector cross product between two Orthogonal Vectors.

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When two vectors are called 'orthogonal' vectors? `color(coral)(text(orth)) + color(deepskyblue)(text(gonia))` means `color(coral)(text(right))+color(deepskyblue)(text(angled))`

- have `90^@` angle between them
- perpendicular to each other
- the vectors are right-angled
- 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`, when the given vectors are orthogonal?

- `|p||q|sin 90 hat n`
- `(|p||q| xx 1)hat n`
- `|p||q|hat n`
- all the above
- all the above

The answer is 'All the above'.

• Magnitude of the cross product of orthogonal vectors is the product of the magnitudes of the vectors.

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

`|vec p xx vec q| = |p||q|`

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