Using Vectors

Two Displacements A hiker walks east from camp for 2.0 km, then northeast for 3.0 km. What is the final displacement of the hiker? Each individual displacement is a vector that can be represented by an arrow. 3.0 km 2.0 km

Graphical Addition The two vectors can be added graphically. The tail of the second vector is placed at the tip of the first. The length and directions are kept the same. The result is the total displacement. It can be measured directly. 4.6 km 3.0 km 2.0 km

Commutative Property Vectors can be shifted as long as they don’t change direction and magnitude. Vectors can be added in reverse order and get the same result.

Parallelogram If two vectors are added from a common origin one can be shifted to make a parallelogram. This is the same as putting the tail to the tip.

Parallel and Antiparallel Vectors that point in the same direction are parallel. Vectors that point in opposite directions are antiparallel.

Cancellation What happens if we add two antiparallel vectors of equal magnitude? The vector sum is a zero length vector. The vectors cancel out.

Vector Subtraction To subtract one vector, add the antiparallel vector instead.

Vector Triangles Three vectors have the same magnitude, L, and form an equilateral triangle. Find They are already tip to tail, so Find Redraw the picture The direction is up The magnitude is 60o Lsin60 next