VECTORS

107 Views

Download Presentation
## VECTORS

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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)