Vectors • In 1 dimension (1D) we can keep track of direction simply by using + or – signs. • In 2 dimensions (2D) or more this is no longer sufficient. – + | | | | | |
Vectors • Recall, we have said that vectors have a magnitude and direction. • i.e. 325 m east • 18 m/s left • 9.8 m/s2 down
Vector Arithmetic • Vector sum: line up vectors tip to tail • Then connect the tail of the first to the tip of the last. A B A+B
Vector Arithmetic • Vector sums are communitive. A+B B B A A B+A
Vector Arithmetic • Vector sums are associative. (A+B)+C A+(B+C) B B+C A+B A B A C C
Vector Arithmetic • The negative of a vector has the same magnitude but the opposite direction as the original vector. -B B
Vector Arithmetic • Thus adding the negative of a vector is the same as subtracting the original vector. A+B -B B A A A -B
Vector Arithmetic • You can also do the vector subtraction by putting the tails together and drawing a vector from minuend (plus side) to subtrahend (minus side). -B B A A A -B A -B
Vectors • Recall that vector sums are communitive. A+B B B A A B+A
Vectors • This suggests that another way of doing vector addition is by using the parallelogram method. A+B B B A A
Vector Components • In fact, we often like to start with one vector and break it up into two components. • We call this resolving the vector.
Vector Components • Typically we resolve a vector into orthogonal components.
Vector Components • Usually we say that the vector is resolved into its x and y components. Y-axis X-axis