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

*click on the content to continue..*

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 dot product as

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

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

- `-(vec p cdot vec q)`
- `|p||q|cos(180+theta)`
- `-|p||q|cos(theta)`
- all the above
- all the above

The answer is 'All the above'

Given the definition of dot product as

`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`

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

- `-(vec p cdot vec q)`
- `p_x(-q_x)+p_y(-q_y)+p_z(-q_z)`
- `-(p_xq_x+p_yq_y+p_zq_z)`
- all the above
- all the above

The answer is 'All the above'

• Dot product with a negative of a vector is the negative of dot product with the vector.

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

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

*Solved Exercise Problem: *

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

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

The answer is '`3i`'

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