Explanation

Scalar multiplication means multiplying a vector by a number.

Example:
2⟨3, 1⟩ = ⟨6, 2⟩

Rules:

• The magnitude changes

• The direction stays the same (unless the scalar is negative)

Negative scalar:
−1⟨2, 3⟩ = ⟨−2, −3⟩
(This reverses direction.)

Quiz

1. What is a scalar?

2. What does 3⟨2, −1⟩ equal?

3. Does scalar multiplication change direction?

4. What happens if the scalar is negative?

5. Does scalar multiplication change magnitude?

Answer Key

1. A number

2. ⟨6, −3⟩

3. Only if negative

4. Direction reverses

5. Yes