1. Vectors Measured quantity with Magnitude and Direction. Example: The wind velocity of 30 knots North The wind velocity of 30 knots North The weight of 140 lbs. down The weight of 140 lbs. down A displacement of 5m West A displacement of 5m West

2. Vector Notation Vector : v or Scalar: V or

3. Vector Addition Parallel vectors behave like numbers on a number line. Parallel vectors behave like numbers on a number line. Add the magnitudes of vectors in the same direction. Add the magnitudes of vectors in the same direction. Subtract the magnitudes of vectors in opposite directions. Subtract the magnitudes of vectors in opposite directions.

4. Graphical Addition Vectors can be added with scaled drawings. Note that vector addition is commutative. Add2Vectors.html Add3Vectors.html The sum of two or more vectors is a Resultant

5. Vector Components In some cases it is easiest way to combine vectors is with components. A Vector Component is the portion of the vector that lies along an x or y axis. We use trigonometry to find these components. phet component addition phet component addition U of T add components U of T add components

6. Unit Vectors All vectors have direction. In many cases it is helpful to define a direction as along an axis. Vectors that perform this service are called Unit Vectors and are used in component notation. Unit vectors are orthogonal or mutually perpendicular. UnitVectors.html

7. Vector Multiplication There are two ways to multiply vectors. They are not interchangeable! The equation used will determine the nature of the product

8. Scalar Product The Scalar or Dot Product is used to multiply only the portion of vectors that are parallel. DotProduct.html

9. Right Hand Rule

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11. Vector Product The Vector or Cross Product is used to multiply vectors and get a vector answer. While it is defined as: There is a more compact way to get an answer with components. The product is always a vector and always orthogonal to A and B. CrossProduct.html RightHandRule.html

12. The Vector product is Anti-Commutative. This means A x B=-B x A RightHandRule.html

13. Find Vector Product with Determinates Matrix algebra provides a compact method for writing and solving cross products. For two vectors A=2i+3j+5k and B=4i-3j+2k. Matrix algebra provides a compact method for writing and solving cross products. For two vectors A=2i+3j+5k and B=4i-3j+2k. We can write AxB as: and calculate the determinant as: i[(3*2)-(5*-3)]-j[(2*2)-(5*4)]+k[(2*-3)-(3*4)] =21i+5j-6k i[(3*2)-(5*-3)]-j[(2*2)-(5*4)]+k[(2*-3)-(3*4)] =21i+5j-6k