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| How do you do the cross product? |
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Definition
[image]
Right hand rule:
i x j = k |
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| How do you find the equation of a line between two points? |
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Definition
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Definition
[image]
[image]
[image]
[image] |
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Term
| Differentiation of the dot product of two functions |
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Definition
[image]
A special case when f(t) = g(t):
[image] |
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Term
| Minimum distance between a point and a line |
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Definition
Point C, Line r = a +[image]
[image]
Point C can be the origin (0,0,0). |
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Term
| Cross product between two vectors, with theta being the angle between |
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Definition
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Term
| How can any vector be represented using the cross product? |
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Definition
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Term
| How do you calculate cross product of a 3x3? |
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Definition
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Term
| Minimum distance between two lines |
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Definition
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Term
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Definition
[image]
Volume is invariant: [a,b,c]=[b,a,c]=[c,b,a]...etc |
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Term
| What does a negative scalar triple product represent? |
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Definition
The vectors a,b,c make up a left handed (non-orthogonal) set.
e.g. [a,c,b] = -[a,b,c] |
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Term
| In general det(A) represents the ratio of the volumes before and after the transformations by A. |
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Definition
If matrix A is multiplied by matrix M, the volume V of matrix A becomes:
V′ = ∣det(M)∣ ⋅ V |
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Term
| Useful rule with regards to a scalar multiple of the scalar product. |
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Definition
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Term
| Find the line between two intersecting planes |
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Definition
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Term
Scenarios when there are three planes
[image] |
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Definition
6) [image], so determinant cannot be 0.
8) Normal vectors are coplanar, thus scalar triple product = 0
7) When the planes in 8 collapse onto one intersecting line. |
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Term
| What are coincident planes? |
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Definition
| Coincident planes means that their normal vectors are parallel and their equations are scalar multiples of each other. |
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