1. Warm UpMay 12 th 1)Find the magnitude and direction of a vector with initial point (-5, 7) and terminal point (-1, -3). 2)Find, in simplest form, the unit vector in the direction of 4i – 2j. 3)Given vector v of magnitude 200 and direction 215°, and vector w of magnitude 150 and direction 162°, find v + w.

2. Homework Questions?

3. A plane is flying on the bearing N 65  E at 500mph. Express the velocity of the plane as a vector. A tailwind is blowing in the direction N 35  E at 80mph. Express the velocity of the wind as a vector. Determine the actual speed and direction of the plane.

4. A plane must actually fly due south at a constant speed of 675mph against a headwind of 60mph blowing in the direction N 15  E. What direction and speed must the pilot maintain to stay on course?

5. The Dot Product = ac + bd Unlike addition and scalar multiplication with vectors, the dot product of vectors is a scalar.

6. Find the dot product of the vectors 1. 2. 3.

7. Let v =, u = and w =. Find the indicated quantity. 1.(uv)w 2.u2v

8. The angle, θ, between two vectors, u and v.

9. Find u v, where φ is the angle between u and v. 1)|u| = 8, |v| = 10, φ = 150°. 2)|u| = 2, |v| = 3, φ = 60° 3)| u | = 4, |v| = 1, φ = 90°.

10. Find the angle between the vectors. 1. and 2. and 3. and

11. If the angle between two vectors is 90°, the vectors are orthogonal (perpendicular).

12. Are the vectors orthogonal, parallel, or neither? 1) and 2) and 3) and

13. Think about it.. What is true about the angle between two nonzero vectors u and v, if the following are true? if u v = 0, then… if u v < 0, then… if u v > 0, then… if v = ku, where k is a scalar, then…

14. Use the dot product to describe the angle between the vectors as acute, obtuse, right, 0 or 180 and explain. and 3i – 4j and -i + 4j and