1.7 - Vectors and Vector Addition

Check my website for online tutoring and to download exercises for the next lesson here: https://learning.withgideon.com/university-physics-1-7x-vectors-and-vector-addition-exercises/ 00:00 Vector Basics Scalars are quantities that have only magnitude or size. Examples include mass, energy and brightness. These can be quantified using only a number and units. Vectors are quantities with both magnitude and direction. Examples include displacement, velocity, acceleration and force. These have both an amount and a direction. 04:28 Representing Vectors We can represent vectors symbolically and graphically. Symbolically we can write down vectors as a letter with an arrow over it. Graphically we can draw an arrow. The direction of the arrow represents the vector direction and the length represents its magnitude: Vectors are parallel when the face the same direction and antiparallel when they face opposite directions. Vectors do not have a fixed position. Rather they are solely defined by their magnitude and direction. This means you can move a vector to a different position and it remains identical, as lot as magnitude and direction are not changed. A negative vector has the same magnitude, but opposite direction as the original vector. Vector Addition There are 2 graphical methods to perform vector addition. 13:55 Parallelogram Method Place vectors A and B together tail to tail and then construct a parallelogram. The resultant vector C starts from the tails and is drawn diagonally to the corner of the parallelogram. 16:00 Head-to-tail or “chain” method Place vectors head to tail, constructing a chain of vectors. The resultant vector C begins from the first tail and is drawn to the final head. Note that in the second method, the order of chaining up the vectors doesn’t matter. This means vector addition is commutative. It is possible to chain up many vectors, head-to-tail, and find a resultant vector for the entire sum graphically: Vector addition is also associative meaning a long chain of vectors like this can be summed up in smaller groups or chunks, and the final sum of the smaller sums will not change. 23:20 Vector Subtraction Vector subtraction is best understood as a type of vector addition where we are adding a negative vector. Graphically we simply need to find the negative of B and then add this to A. 26:03 Vector Multiplication by a Scalar Finally we can multiply a vector with a scalar. A scalar will multiply the magnitude of a vector. Multiplying a scalar will not change the direction of a vector, unless if you are multiplying by a negative scalar. In this case the vector direction will be reversed.