Vectors

• He takes off from Philadelphia International Airport

• He flies 20 miles North• He then flies 10 miles at a

heading 80° East of North• Distance = 30 miles• Result = Resultant =

23.9 miles 24° East of North

Displacement = 23.9 miles 24° East of North

My Brother is a Pilot

• Magnitude - 23.9 miles• Direction - 24° East of North

• Displacement Vector• Vector A equals

Vector A´ (A prime)

• Vector B equalsthe negative of Vector A

A Vector Magnitude and Direction

A+B=B+AVector Addition Commutes

Adding Vectors

Head to Tail Parallelogram Method

Adding Vectors

• The Sum of Two Parallel Vectors

• The Sum of Two Antiparallel Vectors

• Two Add Three Vectors

8

Subtracting Vectors

• A − B

• = A + −B

• 2 A∙

8 8

8 8

Multiplying by a Scalar Same Direction

Twice as Long

Pilots Measure from North

• Clockwise from North• Heading 20°

(20° East of North)• Heading 160° Heading 280 °

Mathematicians and PhysicistsMeasure counterclockwise from the

positive X-axis

• θ = 144° θ = 264°

54° West of North Equals36° North of West