# Vector Calculation

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```					CUSTOMIZE YOUR VECTOR CALC
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VECTOR CALCULATION
Use this sheet to learn how VECTORS describe things in and about the Real World.
If you move one of these vector ARROWS (by grabbing the middle, not the ends) it still represents the same VECTOR, even though the start and end points have changed. Th eA
AY=(+0.82) Yo

A VECTOR is a pretty simple thing: it's just a STRAIGHT LINE with a fixed length and direction. We draw it as an ARROW from one point (the START) to another point (the END). "XY Coordinates": We define a Coordinate System as a set of Independent Dimensions (or Directions). "Unit Vectors" set the Scale in a coordinate system by specifying Units of measurement. Here, we have Position Vectors as Inches in a two dimensional space, with Unit Vectors XO and YO . X X = 1 inch
o

"Basis Vectors" Any Vector has Basis Vectors along each dimension in the coordinate system. Each Basis Vector is Size of the Vector along one of the Unit Vectors. 1.5455 Inches 3.1047 Inches

Y
Yo = 1 inch

A

B
BX = (+3.05) Xo (right)

AX = (-1.31) Xo (left)

CX = (-1.31) + (+3.05) AX = (-1.31)

The order of adding the vectors doesn't affect the result: C is the same Resultant Vector from A+B as from B+A

Or, … start with B, then add A: = BX + AX , CY = BY + AY + CY

>>> CX
C = CX
CX = (+3.05) + (-1.31)

B

BX = (+3.05)

BY=(+0.58)

C

CY=(+0.82) +

The Basis Vectors of a Resultant Vector are the sums, one for each coordinate, of the Basis Vectors of all of the component vectors

AY=(+0.82)

BX = (+3.05)

A

2.

23

C3
3

es ch In

CY=(+0.82) +

Any number of vectors can be added to produce a Vector Sum, also known as a Resultant Vector.

B

<<< Start with A, then add B: CX = AX+BX , CY = AY+BY C = CX + C Y

A

BY=(+0.58) Yo

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Jeff Sperry