Multiply a vector by a scalar

What you'll learn

1. Represent scalar multiplication graphically — scaling the length of a vector and, for negative scalars, reversing its direction.
2. Perform scalar multiplication component-wise: $c(v_x, v_y) = (cv_x, cv_y)$.
3. Compute the magnitude of a scalar multiple using $\|c\mathbf{v}\| = |c|\|\mathbf{v}\|$.
4. Determine the direction of $c\mathbf{v}$: along **v** when $c > 0$, against **v** when $c < 0$, undefined when $c\mathbf{v} = \mathbf{0}$.
5. Construct the unit vector in the direction of a given vector.

Prerequisites

• Recognize and represent vector quantities
• Find components of a vector