lesson #5 continuation

• The tail is the starting position.

• The head is the ending position.

• The magnitude represents how long or large the vector is.

  • For example, a vector representing 100 should be twice as long as a vector representing 50. ​

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​How To Draw a Vector

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• A vector can be multiplied by a number (scalar)

  • For example: In the diagram, the vector (v) can be multiplied by ½, 3, or -2.

    • Notice how (v) changes direction when multiplied by -2​

• There will be times when it's best to treat vectors algebraically, so we create a coordinate system similar to what we've used in the past for a point in 2 or 3 dimensions

• A two-dimension coordinate is written as (x, y). A vector will be written as .

• The position vector is the vector that begins at the origin and goes to the point.

A_x = A*cos(θ)

• Vector addition and subtraction can be done by the parallelogram method or the head to tail method. Vectors that form a closed polygon (cycle) add up to zero

• For the parallelogram method:

1. Draw them at some common point (O)

2. Complete the sides of the parallelogram

3. Then draw the diagonal, this is the result of the addition of the two vectors

• Similar to the parallelogram method

  1. Draw the vectors at a common point

  2. The vector from the tip of -w to v is the result of the subtraction

• It's like adding v and -w

• When resolving vectors in two directions, vectors can be resolved into a pair of perpendicular components.

• Components are defined along an axis (x,y) 

  • The x component of a vector is defined as:

    • M_x = McosΘ

  • The y component of a vector is defined as:

    • M_y = MsinΘ

​Reconstructing a Vector from its Components