Vector Addition Math Example 3

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

Example 3

easy
Add ⟨5,−3⟩+⟨−5,3⟩\langle 5, -3 \rangle + \langle -5, 3 \rangle.

Solution

  1. 1
    ⟨5+(−5),−3+3⟩=⟨0,0⟩\langle 5+(-5), -3+3 \rangle = \langle 0, 0 \rangle.
  2. 2
    These are opposite vectors; their sum is the zero vector.

Answer

⟨0,0⟩\langle 0, 0 \rangle
When a vector is added to its negative (opposite), the result is the zero vector 0\mathbf{0}. This is the additive inverse property of vectors.

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 2 medium

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

Example 4 medium

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

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