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Learning Goal

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Multiply a vector by a scalar

Start lessonBegins with Multiply vector by scalar · Slides

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HSN.VM.B.5
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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.

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1

Multiply vector by scalar

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