11.2 Vectors Review

Vectors

Giving new meaning to mathematics you already know.

Vectors Defined

• A vector is used to indicate a quantity has both magnitude AND direction.

• A vector is represented by an arrow or directed line segment. The length of the arrow represents the magnitude of the vector and the arrow points in the direction of the vector.

• Denoted by either a boldface letter or putting an arrow above the letter

Combining Vectors

• Suppose a particle moves from point A to B

• Then suppose the particle moves from B to C

• Overall, the particle has moved from A to C. This is called the resultant vector and is the result of the sum of the two vectors.

•  $\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC}$  

Combining Vectors cont'd

• We can start with the same vectors, but switch up which one is the starting vector. Turns outs that we would end up at the same point.

• This is known as the Parallelogram Law, as seen in the figure.

Scaling Vectors

• If we don't want to do all that addition but know we need a certain magnitude of a vector, it can be scaled. For instance, it can be doubled, halved, moved in the negative direction, and also moved and scaled.

• By definition, the scalar multiple $c\overrightarrow{v}$  is the vector whose length is c times the length of  $\overrightarrow{v}$  and whose direction is the same if c>0 and is opposite to  $\overrightarrow{v}$  if c<0. If c=0, then the vector is the zero vector.