Lesson 2: Addition and Subtraction of Vectors

• Vector Addition: vectors are added by placing one vector at the end of another and added from head to tail
• the sum of vectors is also known as a resultant vector
• Triangle Law of Vector Addition: 2 vectors arranged from head to tail and the sum is the vector from the tail of the 1st vector to the head of the 2nd vector

  
• Triangle Inequality: the magnitude of the resultant vector has to be less than or equal to the sum of magnitudes of the vector components (e.g. if 2 vectors are equal to 3cm and 4cm, the resultant vector has to have a magnitude of 7cm or less)

  
• the magnitude of the resultant vector is only equal to the sum of vector components if the components are parallel and are in the same direction
• if vectors A and B are parallel and have opposite directions and A is greater than B, that means the magnitude of A + B = A - B and the resultant vector points in the same direction as A
• if vectors A and B are parallel and have opposite directions and B is greater than A, that means the magnitude of A + B = B - A and the resultant vector points in the same direction as B
• the order of vector addition doesn't matter because the resultant will always be the same (B+A = A+B)
• Parallelogram Law of Vector Addition: when 2 vectors are arranged from tail to tail, and the diagonal of the parallelogram is the resultant vector, since the diagonal is where the heads of the 2 vectors meet

  
• In the Parallelogram Method, draw the first vector and place its tail at the origin. Draw the second vector starting from the tail of the first vector. The resultant vector is the diagonal of the parallelogram formed by the two vectors.
• Subtracting a vector is the equivalent of adding its opposite vector
• Subtracting Vectors: connecting the 2 vectors by their tails and the resultant vector starts from the head of the 2nd vector to the head of the 1st vector
• when adding opposite vectors or subtracting equivalent vectors, the resultant vector is a zero vector
• zero vector: has no magnitude and no specific direction