Lesson Plan

Represent scalar multiplication graphically — scaling the length of a vector and, for negative scalars, reversing its direction.

Perform scalar multiplication component-wise: $c(v_x, v_y) = (cv_x, cv_y)$.

Compute the magnitude of a scalar multiple using $|c\mathbf{v}| = |c||\mathbf{v}|$.

Determine the direction of $c\mathbf{v}$: along v when $c > 0$, against v when $c < 0$, undefined when $c\mathbf{v} = \mathbf{0}$.

Construct the unit vector in the direction of a given vector.

HSN.VM.B.5