Addition of Vectors

1. Addition of Vectors • Two methods: • METHOD 1) The head to tail method: • Translate v so that its tail is at the head of u. • Draw the resultant from the tail of u to the head of v.

2. Addition of Vectors • Two methods: • METHOD 2) The Parallelogram Method: • Translate v so that u and v are tail to tail. • The resultant is a diagonal of the parallelogram.

3. Subtraction of Vectors • Two methods: • METHOD 1) The head to tail method: • Draw the opposite of v and then translate it so that its tail is at the head of u, therefore drawing u+ (- v).

4. Subtraction of Vectors • Two methods: • METHOD 2) The tail to tail method: • Translate v so that u and v are tail to tail. • The resultant is the vector from the head of v to the head of u.

5. The ZERO vector • This vector is defined as having zero magnitude and no specific direction. It is the resultant of adding two opposite vectors. • u + (-u) = 0

6. Example: • Sketch • a) a + b b) b – c c) b + c - a c b a

7. Example: • p.325 #3

8. Example: • p.325 #4

9. Example: • Bugs Bunny travels 100 km [N] and then 150 km [E]. What is his displacement?

10. Example: • Iggy the inchworm travels 5cm[W], then 9cm at a bearing of 100 degrees, and finally 5cm[S]. What is his final displacement?

11. TREASURE HUNT CHALLENGE: • You must hide a golden ticket somewhere in the school that another team of students must find so that they can cash it in for a prize. • Rules: • There must be 10 direction vectors written down on one sheet that when added or subtracted lead to the golden ticket. • 5 of the vectors must be added and 5 must be subtracted • 5 of the vectors must be expressed with a true bearing and 5 with a quadrant bearing • There can be a maximum of 4 bearings of N,S,E or W • Magnitudes must be expressed in paces