In this page, you will learn about the vector cross product with the negative of a vector.

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Given `vec p = 2i+j-k` what is the negative of `vec p`?

- `2i+j-k`
- `-2i-j+k`
- `-2i-j+k`

The answer is '`-2i-j+k`'

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)`?

- `-(vec p xx vec q)`
- `|p||q|sin(180+theta) hat n`
- `-|p||q|sin(theta) hat n`
- all the above
- all the above

The answer is 'All the above'

Given the definition of cross product as

`vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`

What is `vec p xx (-vec q)`?

- `-(vec p xx vec q)`
- `|(i, j, k),(p_x, p_y, p_z),(-q_x, -q_y, -q_z)|`
- `-|(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`
- all the above
- all the above

The answer is 'All the above'

• Cross product with a negative of a vector is the negative of cross product with the vector.

**Cross Product with the negative: ** For any vectors `vec p, vec q`

`vec p xx (-vec q) = -(vec p xx vec q)`

*Solved Exercise Problem: *

Given `vec p xx vec q = -3i` what is `(-vec p) xx vec q`?

- `3i`
- `3i`
- `-3i`
- `i`
- `3`

The answer is '`3i`'

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