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| start [2017/03/29 15:20] – rupert | start [2017/04/25 09:19] (current) – [Notes by lecture] rupert | ||
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| * using EROs to find the inverse of a square matrix | * using EROs to find the inverse of a square matrix | ||
| * (column) vectors as instructions to move points | * (column) vectors as instructions to move points | ||
| - | /* * [[Lecture 17]] - Tuesday 4 March 2017 | + | |
| + | * [[Lecture 17]] - Tuesday 4 March 2017 | ||
| * the vector $\vec{AB}$ which moves point $A$ to point $B$ | * the vector $\vec{AB}$ which moves point $A$ to point $B$ | ||
| * the length $\|\vec v\|$ of a vector $\vec v$ | * the length $\|\vec v\|$ of a vector $\vec v$ | ||
| Line 110: | Line 111: | ||
| * Addition of vectors: the triangle and parallelogram rules | * Addition of vectors: the triangle and parallelogram rules | ||
| * [[Lecture 18]] - Thursday 6 April 2017 | * [[Lecture 18]] - Thursday 6 April 2017 | ||
| - | * The dot product | + | * The dot product |
| + | * The geometric | ||
| * Calculating angles | * Calculating angles | ||
| - | * The orthogonal projection of one vector onto another | + | |
| * [[Lecture 19]] - Tuesday 11 April 2017 | * [[Lecture 19]] - Tuesday 11 April 2017 | ||
| + | * The orthogonal projection of one vector onto another | ||
| * The cross product of vectors in $\mathbb{R}^3$: | * The cross product of vectors in $\mathbb{R}^3$: | ||
| * The area of a triangle using the cross product | * The area of a triangle using the cross product | ||
| Line 119: | Line 122: | ||
| * Geometry of the cross product: areas and volumes | * Geometry of the cross product: areas and volumes | ||
| * Planes in $\mathbb{R}^3$ and their normal vectors | * Planes in $\mathbb{R}^3$ and their normal vectors | ||
| + | |||
| * [[Lecture 21]] - Tuesday 18 April 2017 | * [[Lecture 21]] - Tuesday 18 April 2017 | ||
| - | * Orthogonal | + | * Parallel |
| * Examples: finding the equations of planes with various properties | * Examples: finding the equations of planes with various properties | ||
| - | * The distance from a point to a plane | ||
| * [[Lecture 22]] - Thursday 20 April 2017 | * [[Lecture 22]] - Thursday 20 April 2017 | ||
| + | * The distance from a point to a plane | ||
| * The distance between planes | * The distance between planes | ||
| * The parametric equation of a line | * The parametric equation of a line | ||
| - | * The distance from a point to a line (using the cross product) | + | |
| * [[Lecture 23]] - Tuesday 25 April 2017 | * [[Lecture 23]] - Tuesday 25 April 2017 | ||
| + | * The distance from a point to a line (using the cross product) | ||
| * The distance from a point to a line (using orthogonal projection) | * The distance from a point to a line (using orthogonal projection) | ||
| - | * The distance between | + | * The distance between lines in $\mathbb{R}^3$ |
| - | */ | ||
| Line 154: | Line 159: | ||
| * [[https:// | * [[https:// | ||
| * [[https:// | * [[https:// | ||
| - | / | + | |
| * [[https:// | * [[https:// | ||
| * [[https:// | * [[https:// | ||
| Line 162: | Line 167: | ||
| * [[https:// | * [[https:// | ||
| * [[https:// | * [[https:// | ||
| - | | + | / |
| */ | */ | ||
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