Vectors Day 2

1
Vectors Day 2

• Objective Be able to find and work with
  directional angles for vectors.
• TS Develop a capacity for working within
  ambiguity.
• Warm Up
• Given the below vectors find 2u 3v

2
Directional Angles

• Given a vector, v, its direction angle is the
  angle formed with the positive x-axis.
• Thus v v ltcos?, sin?gt or ltvcos?,
  vsin?gt
• v(cos?)i v(sin?)j
• So, given a vector lta,bgt as shown,
• one way to get the direction angle
• would be to use the tangent ratio

b
?
a
3
Find the Directional Angle of the vector.

• 1) u 3i 3j

4
Find the Directional Angle of the vector.

• 2) v 3i 4j

5

• 3) Write a linear combination of the standard
  unit vectors i and j, where the initial point is
  (-1, -5) and the terminal point is (2, 3).

6

• 4) Find the component form and make a sketch of v
  u 2w, where u 2i - j and w i 2j

7

• 5) Find the magnitude and direction angle of
• v 8(cos135i sin135j)

8

• 6) Find the component form of v with a magnitude
  of 3v2 and that makes an angle of 150 with the
  positive x-axis.

9

• 7) Find the component form of u v where
  u 35, v 50 and where the direction
  angles are ?u30 and ?v120