To rotate a 2D vector by 90 degrees clockwise, you can use a simple trick.
Understanding 90-Degree Vector Rotation
Typically, vector rotation involves matrix mathematics. However, a simpler method exists for rotating 2D vectors 90 degrees clockwise, as referenced from this source (Note: this is a placeholder and the original date and source was provided in the instructions).
The Simple Trick
Here's the process, broken down into two steps:
- Negate the X component: Multiply the x-value of your vector by -1.
- Swap the X and Y values: Switch the positions of the modified x-value and y-value.
Example
Let's say you have a vector represented as (x, y). Following the steps above:
- Original Vector: (x, y)
- Step 1: (-x, y)
- Step 2: (y, -x)
Therefore, the resulting vector after rotating the original vector 90 degrees clockwise will be (y, -x).
Table Representation
| Step | Original Vector | Transformation | Resulting Vector |
|---|---|---|---|
| Initial State | (x, y) | - | (x, y) |
| Negate X Component | (x, y) | x = -x | (-x, y) |
| Swap Components | (-x, y) | Swap x and y | (y, -x) |
Practical Application
- Consider a vector
(2, 3). - Following the steps, we first negate x, making it
(-2, 3). - Then, we swap x and y values, getting
(3, -2). - So the original vector (2,3) rotated 90 degrees clockwise becomes (3,-2).
Summary
Rotating a 2D vector by 90 degrees clockwise is achieved by negating the x-component and then swapping the x and y values. This is a simplified approach that avoids complex matrix calculations.
