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Scalar Multiplication of Vectors Calculator

Online scalar multiplication: multiply a vector by λ; length scales and direction follows the sign.

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λa=(λx,λy)
Vector a
x
y
Sign sets direction

📖 Tutorial | Scalar Mult

1. Definition
Multiplying a vector by a scalar: λa=(λx,λy), length |λ||a|; λ>0 same direction, λ<0 opposite.
2. Formula & Notation
λScalar
3. Properties & Laws
  • Length scales by |λ|;
  • Sign sets direction;
  • λ=0 gives zero;
  • Associative, distributive.
4. Steps
  1. Enter vector and λ;
  2. Click "Multiply";
  3. Or click "Load Example".
5. Worked Examples
Example: 2(3,4): (6,8).
6. Common Pitfalls
Negative flips;
Zero scalar;
Scale both components.

❓ FAQ | Scalar Mult

Result?
(λx,λy).
Length?
|λ||a|.
Direction?
Negative flips.
λ=0?
Zero.
Example?
(6,8).
Normalize?
1/|a|.