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⟩
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