Adding & Subtracting Vectors (DP IB Analysis & Approaches (AA)): Revision Note

Adding & Subtracting Vectors

How are vectors added and subtracted numerically?

• The sum of two or more vectors is called the resultant of the vectors

  • The resultant is also a vector

• To add two vectors, you add together the corresponding components

• To subtract two vectors, you subtract together the corresponding components

• It is easy to add and subtract column vectors

  • For example, 

• Collect like-terms if working with vase vectors

  • For example, (2i + j – 5k) – (i + 4j + 3k) = (i – 3j – 8k)

How are vectors added and subtracted geometrically?

• Vectors can be added geometrically by joining the end of one vector to the start of the next one

• The resultant vector will be the shortest route from the start of the first vector to the end of the second

• If the two vectors have the same starting position

  • The second vector can be translated to the end of the first vector to find the resultant vector

  • This results in a parallelogram with the resultant vector as the diagonal

•  Subtracting a vector is the same as adding a vector with its direction reversed

  • For example, a – b = a + (-b)