The Triangle Method

The triangle method, also called tip-to-tail method, is a way to find the sum of two or more vectors. As an example, consider the following vectors whose component forms are a = ⟨ -1,2 ⟩ and b=⟨ 3,2 ⟩.

Apply the following two steps to find the sum of a and b.

1

Join the Vectors

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Translate b so that the tail of b touches the tip of a.

2

Draw the Resultant

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Draw a vector from the tail of a to the tip of b. This vector is the sum of a and b.

Here it can be seen why the method is called the triangle method. Notice that the component form of the resultant is ⟨ 2,4 ⟩ and it coincides with the vector addition of a and b. a + b &= ⟨ -1,2 ⟩ + ⟨ 3,2 ⟩ &= ⟨ -1+3,2+2 ⟩ &= ⟨ 2,4 ⟩