Section 6.1 & 6.2 VECTORS
“still” measurements “moving” measurements Force Velocity Acceleration • Temperature • Distance • Height • Area • Volume
Vector • A directed line segment (arrow) with its head tale at the origin and its head at the point (a, b) • Represents both direction & magnitude Vector with components a & b
Magnitude • The “amount of something” (i.e. force& speed) • Magnitude = length of the vector
Vectors that are the same length and the same direction are equivalent “component vector”
Ex 1) Draw the directed line segment from R(-4,7) to S(-1,5) Component Vector: Magnitude: Linear Combination:
Ex 2) Draw the directed line segment from P=(1,-2) to Q=(3,4) Component Vector: Magnitude: Linear Combination:
Dot Product • A way of “multiplying” vectors • Answer is a real number
Orthogonal: perpendicular (90°) • Dot product will equal ZERO u v
Ex 3) Perform each vector operation a.)u + v b.) 3u c.) u+(-2)v d.) u ∙ v
Adding Vectors Graphically Graph Head to Tail v u u+v
Ѳ is called the “direction angle” Magnitude y -vertical Ѳ x -horizontal
Ex 6) Find the horizontal &vertical components of vector vwith direction angle 25° and magnitude 18
“Magnitude” • Velocity (speed) • Gravity (force)
Ex 8)Hector is trying to get his dog to keep walking. He pulls on the leash with a force of 67 Newton's, at an angle of 30 degrees above the horizontal. Determine the vertical and horizontal components of the vector.
What is the component form of the directed line segment from P(-1, 5) Q(4, 2)?
Find the horizontal & vertical components of a vector with a magnitude of 12 and direction angle of 35°
What is the direction angle of a vector with a magnitude of 10 and a horizontal component of 5?
1. Helen is parasailing. She sits in a seat harness which is attached by a tow rope to a speedboat. The rope makes an angle of 51° with the horizontal and has a tension of 350 N. Determine the horizontal and vertical components of the tension force.
2. A plane is flying on a bearing of 65° at 500 mph. Find the component form of the velocity of the airplane *Bearing is the angle formed with due north measure clockwise
Vector Equations of Lines Equation of a line passing through v
#12 a. (-2, 5) and (4, 2) b. (3, 4) and (6, -3)