Vectors in Two Dimensions
7.2 Vectors in two dimensions – Cheat Sheet
1. Translation using a vector
- A translation moves every point by the same vector.
- Represented as AB, a, or in column form:
[ x ]
[ y ]
where:
- x = horizontal change (positive → right, negative → left)
- y = vertical change (positive → up, negative → down)
Example: Translation by
[ 3 ]
[ 2 ]
means move 3 units right and 2 units up.
2. Adding vectors
- Add corresponding components.
Example:
[ 4 ] [ 1 ] [ 5 ]
[ 3 ] + [ 2 ] = [ 5 ]
3. Subtracting vectors
- Subtract corresponding components.
Example:
[ 6 ] [ 2 ] [ 4 ]
[ 5 ] - [ 3 ] = [ 2 ]
4. Multiplying a vector by a scalar
- Multiply each component by the scalar.
Example:
3 × [ 2 ] [ 6 ]
[-4 ] = [ -12 ]
5. Equal vectors
- Same magnitude and direction.
Example:
[ 2 ]
[ 5 ]
is equal to
[ 2 ]
[ 5 ]
6. Negative vectors
- Reverse the direction by multiplying by –1.
Example:
- [ 3 ] [ -3 ]
[-4 ] = [ 4 ]