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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

Test your knowledge with interactive flashcards

Can scalar multiplication produce a zero vector?

Click to reveal answer

Yes, multiplying any vector by zero results in the zero vector, which has no magnitude or direction.

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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