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**1. **Vector and Scalars

**2. **Scalars versus Vectors Scalar: A quantity that has a magnitude but no direction.
Vector: A quantity that has both a magnitude (displacement) and direction.
Vectors can be represented graphically or algebraically.

**3. **Quick Conventions II The Glencoe Physics book will define vectors by color:
Displacement (m)
Velocity (m/s)
Acceleration (m/s2) Force (N)
Momentum/Impulse

**4. **Vector and Scalars

**5. **Scalars versus Vectors Scalar: A quantity that has a magnitude but no direction.
Vector: A quantity that has both a magnitude (displacement) and direction.
Vectors can be represented graphically or algebraically.

**6. **Representing Vectors Example: Displacement
Graphically= actually drawing an arrow
Algebraically = numerical value

**7. **Graphically Representing Vectors Magnitude
Magnitude is drawn as an arrows length.
Longer arrows, larger magnitude.

**8. **Direction Graphically direction is represented by an arrow (tip to tail).
N, S, E, W: Cartesian Coordinate System.
Direction can be broken down into two parts:

**9. **Adding vectors=tip to tail Say we have two vectors a and b.
To add them:
Reposition one of the vectors so that the tip of one touches the tail of the other.
Make a new vector going from the tail of the open end to the point of the other end.

**10. **Graphically adding vectors

**11. **Adding multiple vectors

**12. **Subtracting vectors Say we have two vectors a and b.
To subtract them (a-b):
Redraw vector b so that it has the opposite direction. (flip the tip and tail)
Add the vectors as normal.

**13. **Visually subtracting vectors

**14. **Vector Examples Remember all vectors need a magnitude and direction.
Measure direction with a protractor.

**15. **Quick Conventions I Take a look at this vector:
30° N of E
60° E of N
While both are correct always put the protractor on the horizontal axis (EW) and measure to the north or south.

**16. **Graph Vectors Practice Pg 77-78
Problems: 1-5, 12, 20, 22

**17. **Vector and Scalars

**18. **Algebraically Representing Vectors Magnitude
magnitude is assigned a number value.
The magnitude should still have a unit such as 15-m.

**19. **Direction Algebraically direction is represented with degrees.
use the form x° N/S of E/W
Protractor should be lined up on the horizon
No radians (check your calculator)

**20. **Breaking Down Vectors If you have a vector you can break it down into an x and y component.
This is useful for adding.

**21. **Using Trig for Direction Useful formulas for 90° vectors:
a2 + b2 = c2
sin ? = a/c
cos ? = b/c
tan ? = a/b
Remember:
DEGREE’s
FYI: For non 90°
r2 = a2 + b2 +2abcos ?.

**22. **Using Trig for Direction TRIG PNEMONIC
sin ? = o/h
cos ? = a/h
tan ? = o/a
Remember:
SOA CAH TOA

**23. **Basic math and vectors vector + or - vector = vector
vector x vector = scalar
vector / vector = not done
vector + or - scalar = can’t do
vector x or / scalar = vector

**24. **Vectors and scalars When multiplying or dividing a vector by a scalar you only need to know two things:
Either multiply or divide the magnitude of the vector.
If the scalar is a negative number, reverse the direction of the vector.

**25. **Multiplying Vectors Multiplying vectors together is also called the dot product
Calculus III: a • b = ||a|| ||b|| cos (?).
Why do we need to know this?
Force is defined as mass x acceleration
Mass is a scalar, accel is a vector.
Force therefore is a vector. (needs direction)
Energy is defined as Force x distance.
Force is a vector and distance is a vector.
Energy therefore is a scalar. (no direction)

**26. **Trig Practice Problems Worksheet
Practicing Pythagoras
Trigonometry Word Problems