Vector Addition Math Example 2

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

Example 2

medium
Find u+v+w\mathbf{u} + \mathbf{v} + \mathbf{w} where u=⟨1,−2,3⟩\mathbf{u} = \langle 1, -2, 3 \rangle, v=⟨0,5,−1⟩\mathbf{v} = \langle 0, 5, -1 \rangle, w=⟨−3,1,2⟩\mathbf{w} = \langle -3, 1, 2 \rangle.

Solution

  1. 1
    Step 1: Add xx-components: 1+0+(−3)=−21 + 0 + (-3) = -2.
  2. 2
    Step 2: Add yy-components: −2+5+1=4-2 + 5 + 1 = 4.
  3. 3
    Step 3: Add zz-components: 3+(−1)+2=43 + (-1) + 2 = 4.
  4. 4
    Result: ⟨−2,4,4⟩\langle -2, 4, 4 \rangle.

Answer

⟨−2,4,4⟩\langle -2, 4, 4 \rangle
Vector addition extends naturally to 3D (and beyond) — just add each component separately. The operation is both commutative (u+v=v+u\mathbf{u} + \mathbf{v} = \mathbf{v} + \mathbf{u}) and associative.

About Vector Addition

Vector addition combines vectors component-wise or head-to-tail to produce a resultant vector.

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More Vector Addition Examples

Example 1 easy

Add [formula].

Example 3 easy

Add [formula].

Example 4 medium

A boat travels [formula] km then [formula] km. What is the total displacement?

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