Vector Scalar Multiplication
Multiply a vector by a scalar k and get the result vector plus the original and scaled norms. Any dimension.
Input
Multiply each component of a vector by a scalar k to get the result vector and how its norm changes.
Vector components
Result
Result vector k·v
(6, 8, 0)
Original norm |v|
5
Scaled norm |k·v|
10
Scalar k
2
Component-by-component
| Component | Original | Scaled (×k) |
|---|---|---|
| Component 1 | 3 | 6 |
| Component 2 | 4 | 8 |
| Component 3 | 0 | 0 |
How it works
- Each component is multiplied by the scalar k to form the result vector k·v = (k·v1, k·v2, …, k·vn).
- The norm is the Euclidean norm, the square root of the sum of squared components: |v| = √(v1² + … + vn²).
- Scalar multiplication scales the norm by |k|, so the scaled norm equals |k|·|v|.
- A negative k reverses the direction and flips the sign of every component. When k = 0 the result is the zero vector.
- Use the add and remove buttons to work with vectors of any dimension.
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Vector Scalar Multiplication