Vector Addition Math Example 1

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

Example 1

easy
Add ⟨2,1⟩+⟨−1,3⟩\langle 2, 1 \rangle + \langle -1, 3 \rangle.

Solution

  1. 1
    Step 1: Add corresponding components: (2+(−1),1+3)(2 + (-1), 1 + 3).
  2. 2
    Step 2: =⟨1,4⟩= \langle 1, 4 \rangle.
  3. 3
    Check: Geometrically, this is the diagonal of a parallelogram formed by the two vectors ✓

Answer

⟨1,4⟩\langle 1, 4 \rangle
Vector addition is done component-wise: add the xx-components together and the yy-components together. Geometrically, it's the tip-to-tail method or the parallelogram diagonal.

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 2 medium

Find [formula] where [formula], [formula], [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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