H2 Math Summary Notes

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Pure Mathematics
Unit 1 Inequalities
Basics of Test Point Method
Unit 2 Graphing Techniques
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Unit 3 Transformation of Graphs
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Unit 4 Functions
Conceptual Video
How to Use GC to Plot an Inverse Graph
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Unit 5 APGP & Recurrence Relations
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Unit 6 Sigma Notation
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Unit 7 Techniques of Differentiation
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Unit 8 Applications of Differentiation
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Unit 9 Maclaurin Series
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Unit 10 Techniques of Integration
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Unit 11 Applications of Integration
Conceptual Video
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Unit 12 Differential Equations
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Unit 13 Vectors
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Unit 14 Complex Numbers
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Statistics
Unit 15 Permutation and Combinations
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Unit 16 Probability
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Unit 17 Discrete Random Variable
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Unit 18 Binomial Distribution
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Unit 19 Normal Distribution
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Unit 20 Sampling and Estimation
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Unit 21 Hypothesis Testing
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Unit 22 Correlation and Linear Regression
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Unit 13.2 Worked Example 2

H2 Math Summary Notes Unit 13 Vectors Unit 13.2 Worked Example 2

The line [latex]{{l}_{2}}[/latex] passes through [latex]A\left( 3,1,-2 \right)[/latex] and is parallel to the direction vector [latex]\left( \begin{matrix}7  \\15  \\1  \\\end{matrix} \right)[/latex].

[latex]{{l}_{2}}[/latex] intersects [latex]{{l}_{1}}:\mathbf{r}=\left( \begin{matrix}  -12  \\ -22  \\ 11  \\\end{matrix} \right)+\lambda \left( \begin{matrix}4  \\ 4  \\ -7  \\\end{matrix} \right);\lambda \in \mathbb{R}[/latex] at [latex]C[/latex].

Find

(i)

the coordinates of [latex]C[/latex],

(ii)

the acute angle between [latex]{{l}_{1}}[/latex] and [latex]{{l}_{2}}[/latex],

(iii)

the vector line equation of mirror image of [latex]{{l}_{2}}[/latex] in [latex]{{l}_{1}}[/latex]. 

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