Section 6.1: Vectors in a Plane

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Presentation transcript:

Section 6.1: Vectors in a Plane Do Now (5 min. – No Talking First 4!) Draw a ray that starts at (1,0) and contains (4,4) What is the length of the segment that connects these points? Draw another ray with the same length but goes in the opposite direction. What are the coordinates of the end point of this ray?

Vectors: Directed Line Segments Vectors are equivalent if they have the same distance (magnitude) and slope (direction).

Component Form of a Vector Rather than writing a vector as a segment with endpoints, write in component form by shifting the vector so that its tail is at the origin. Process:

Simple Algebra with Vectors Given , find… 3v -2w v + w w – v 4w – 5v

Vectors as Multiples of i and j

Unit Vectors

Component Form from a Graph Given θ and |v|, .

Finding magnitude and direction angles. Sketch each vector. Create a right triangle. Use distance and right triangle trig.

Applications of Vectors Note: Navigation is measured from due north. To complete this question, draw a sketch. Then, create a right triangle w/ a westerly component and a northerly component. Use right triangle trig to find values for these components.