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| Conceptual Definition of elipses |
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Definition
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Definition
[image]
[image]
[image]
[image] |
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| Definition of a Hyberbola |
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Definition
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Definition
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Definition
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Definition
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| Definition of vector addition |
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Definition
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| definition of scalar multiplication |
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Definition
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| Definition of a component vector |
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Definition
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| Magnitude or length of a vector |
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Definition
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Term
| vector addition with position vectors |
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Definition
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Definition
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Definition
[image]
[image]
[image]
[image] |
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| Definition of a dot product |
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Definition
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| Properties of dot products |
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Definition
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| Cosine Theorem for the angle between vectors and Corrolary |
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Definition
[image]
[image]
[image]
[image] |
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| Othaganal vectors, including orthoganal vector from scalar projection |
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Definition
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Definition
[image]
[image][image][image] |
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Term
| definition of a cross product |
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Definition
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Definition
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| Definition of a cross product using determinates and unit vectors |
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Definition
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Term
| Coss product orthoganal Theorem |
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Definition
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Term
| Cross product magnitude, area of a parallelogram Theorem and corrolary |
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Definition
[image]
[image]
[image][image]
[image] |
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| Unit vector properties of cross products |
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Definition
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Term
| Properties of cross products |
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Definition
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Term
Scalar triple product
[image] |
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Definition
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Term
| Volume of a parallelepiped |
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Definition
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| Simpler Vector equation of a line |
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Definition
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Definition
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| Symetric equations of a line and the definition of direction numbers |
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Definition
[image]
[image]
[image]
[image] |
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Term
| Formal definition of a vector equation of a line |
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Definition
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Term
| vector equations of a plane with n as the normal vector |
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Definition
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| Scalar equation of a plane |
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Definition
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Definition
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Definition
[image]
[image]
[image][image] |
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Definition
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Definition
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| Hyperboloid of Two Sheets |
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Definition
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Term
| Professors algorithm for classifying cubics |
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Definition
Given an equation of degree 2:
if(a variable is missing ){
it is a cylinder or no solution
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if(2 variables appear strictly linear){
you have a cylinder
}
if(have up to a translation: Ax²+ By²+Cz²=D){
if(D== 0){
if(A,B,C same sign)
get a point
if(A,B,C have different signs)
You have a cone
}
if (D != 0){
Standard form = Ax²+By²+Cz² = 1
Put equation in standard form
if(numberOfNegativeSigns == 0)
ellipsoid
if(numberOfNegativeSigns == 1)
1-sheet hyperboloid
if(numberOfNegativeSigns == 2)
2-sheet hyperboloid
if(numberOfNegativeSigns == 3)
no solutions
}
}
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Definition
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