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Apply scalar multiplication of vectors

Geometry and measures • Vectors

Key concepts

What you'll likely be quizzed about

  • Scalar multiplication involves the multiplication of a vector by a number, called a scalar.
  • For a vector \( \mathbf{v} = [v_1, v_2] \) and a scalar \( k \), the result is \( k \cdot \mathbf{v} = [k \cdot v_1, k \cdot v_2] \).
  • This process affects the vector's length but preserves its direction when the scalar is positive.

Flashcards

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What does a negative scalar do to a vector?

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A negative scalar reverses the vector's direction and alters its magnitude depending on the absolute value of the scalar.

Key notes

Important points to keep in mind

A positive scalar lengthens the vector.

A negative scalar reverses the direction.

Multiplication by zero gives the zero vector.

Scalars affect only magnitude, not direction.

Use scalar multiplication to solve vector problems efficiently.

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