3. Addition and subtraction of vectors





Another way to define addition of two vectors is by a headtotail construction that creates two sides of a triangle. The third side of the triangle determines the sum of the two vectors, as shown below. Place the tail of the vector v at the head of the vector u. That is, u = and v = . Now construct the vector to complete the third side of the triangle OAP.
This method is equivalent to the parallelogram law of addition, as can be easily seen by drawing a copy of v tailtotail with u, to obtain the same parallelogram as before. Using position vector notation, the triangle rule of addition is written as follows: for any three points X, Y , Z, Both the triangle and the parallelogram rules of addition are procedures that are independent of the order of the vectors; that is, using either rule, it is always true that u + v = v + u for all vectors u and v. This is known as the commutative law of addition. There are other rules like this one, and they are discussed in the component Vector Algebra.


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