1. Vector Algebra
Using î and ĵ

2. Before now, we described the x and y components of a vector simply as x = ? and y =?.
We will start using “unit vectors” with special symbols ĵ and î pronounced “j hat” and “i hat”

3. Î “ i hat” represents the x- direction
Ĵ “j hat” represents the y-direction

4. Example 1
A rabbit escaping from a fox runs 10.0 m/s at 40.0°north of west. Calculate the rabbits velocity in terms of components and unit vectors.
**Setting up a right triangle we should be able to use trig to calculate the vx and Vy

5. Example 1 cont. Vx is -7.66m/s Vy is 6.43 m/s
Therefore the velocity unit vectors can be noted as (-7.66î ĵ) m/s

6. Example 2
A bird flew 100m west then turned 45° north of west and flew 200m. Use algebraic addition of vectors to find the birds net displacement.
Vector A is -100îm
Vector B is Bx + By = (-141î + 141ĵ)m

7. Example 2 cont.
Vector C (resultant) can be found by adding î and ĵ parts of vectors A and B
Vector C is -100îm + (-141î + 141ĵ)m
Rearrange so…-100î + (-141î) ĵ
Therefore ( -241î + 141ĵ)m are the components

8. Example 2 cont. C2 = Cx2 + Cy2 C = √ (xî2 + yĵ2) C= √ (-2412 + 1412)
C= 279m

9. Example 2 cont. The angle of displacement is then calculated using:
Θ = tan-1 ( Cy / Cx)
Θ = tan-1 (yĵ /xî)
Θ = tan-1(141/241) = 74°
Finally, Vector C is 280m, 30.36° north of west