To add or subtract two vectors, add or subtract the corresponding components.
Let be two vectors.
Then, the sum of is the vector
The difference of is
The sum of two or more vectors is called the resultant. The resultant of two vectors can be found using either the parallelogram method or the triangle method.
Draw the vectors so that their initial points coincide. Then draw lines to form a complete parallelogram. The diagonal from the initial point to the opposite vertex of the parallelogram is the resultant.
Draw the vectors one after another, placing the initial point of each successive vector at the terminal point of the previous vector. Then draw the resultant from the initial point of the first vector to the terminal point of the last vector. This method is also called the head-to-tail method .
By the definition of vector addition, Substitute the given values of u1 , u2 , v1 and v2 into the definition of vector addition.
We know that the difference u – v is equivalent to the sum u + (– v ). We will need to determine the components of – v .
Recall that – v is a scalar multiple of –1 times v . From the definition of scalar multiplication, we know:
Substituting the given values of the components of v , we obtain
Substitute the values of the components of u and – v into the definition of vector addition.
We substitute the values of the components of u and – v into the definition of vector addition and simplify: