Vector Addition, Subtraction, and Scalar Multiplication Math Example 2

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

Example 2

medium
Find u−v\mathbf{u} - \mathbf{v} where u=⟨2,5,−1⟩\mathbf{u} = \langle 2, 5, -1 \rangle and v=⟨4,−3,2⟩\mathbf{v} = \langle 4, -3, 2 \rangle.

Solution

  1. 1
    Step 1: Subtract component-wise: (2−4,5−(−3),−1−2)(2-4, 5-(-3), -1-2).
  2. 2
    Step 2: =⟨−2,8,−3⟩= \langle -2, 8, -3 \rangle.
  3. 3
    Check: u−v\mathbf{u} - \mathbf{v} is the vector from v\mathbf{v}'s tip to u\mathbf{u}'s tip ✓

Answer

⟨−2,8,−3⟩\langle -2, 8, -3 \rangle
Vector subtraction u−v\mathbf{u} - \mathbf{v} can be thought of as u+(−v)\mathbf{u} + (-\mathbf{v}). Geometrically, it points from v\mathbf{v} to u\mathbf{u}.

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 3 medium

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

Example 4 easy

Compute [formula].

Example 5 medium

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

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