Vector Addition, Subtraction, and Scalar Multiplication Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

easy
Compute −3⟨2,−4⟩-3\langle 2, -4 \rangle.

Solution

  1. 1
    −3⋅⟨2,−4⟩=⟨−6,12⟩-3 \cdot \langle 2, -4 \rangle = \langle -6, 12 \rangle.
  2. 2
    Each component is multiplied by −3-3.

Answer

⟨−6,12⟩\langle -6, 12 \rangle
Negative scalar multiplication reverses the direction of the vector while scaling its magnitude by ∣−3∣=3|{-3}| = 3.

About Vector Addition, Subtraction, and Scalar Multiplication

Vectors are added and subtracted component by component. Scalar multiplication multiplies each component of a vector by a number. If u=⟨u1,u2⟩\mathbf{u} = \langle u_1, u_2 \rangle and v=⟨v1,v2⟩\mathbf{v} = \langle v_1, v_2 \rangle, then u+v=⟨u1+v1,u2+v2⟩\mathbf{u} + \mathbf{v} = \langle u_1 + v_1, u_2 + v_2 \rangle and ku=⟨ku1,ku2⟩k\mathbf{u} = \langle ku_1, ku_2 \rangle.

Learn more about Vector Addition, Subtraction, and Scalar Multiplication →

More Vector Addition, Subtraction, and Scalar Multiplication Examples

Example 1 easy

If [formula] and [formula], find [formula].

Example 2 medium

Find [formula] where [formula] and [formula].

Example 3 medium

Given u = <2, -1> and v = <3, 5>, find 2u - v and its magnitude.

Example 5 medium

Find the vector from point [formula] to point [formula].

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