Vector Addition Math Example 4

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Example 4

medium
A boat travels ⟨4,3⟩\langle 4, 3 \rangle km then ⟨−1,5⟩\langle -1, 5 \rangle km. What is the total displacement?

Solution

  1. 1
    Total displacement = ⟨4+(−1),3+5⟩=⟨3,8⟩\langle 4 + (-1), 3 + 5 \rangle = \langle 3, 8 \rangle km.
  2. 2
    The boat is 3 km east and 8 km north of its starting point.

Answer

⟨3,8⟩\langle 3, 8 \rangle km
Displacement vectors add tip-to-tail. The resultant vector gives the net displacement regardless of the path taken — a key application of vector addition in physics and navigation.

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 3 easy

Add [formula].

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