Practice Symmetric Form (5.2) - 3D Geometry - IB 10 Mathematics

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6 sample questions

Question 1.
Write the symmetric form for a line passing through (1,2,3) and parallel to (4,5,6).
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Start with the coordinates of the point and the direction ratios.
Question 2.
What do the direction ratios of a symmetric line represent?
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Remember, these ratios help define the slope of the line in three dimensions.
3Question 3.
What is the symmetric form of a line in 3D?
- r = |p - q|
- x - x0/a = y - y0/b = z - z0/c
- None of the above
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It eliminates the parameter.
4Question 4.
True or False: The direction ratios can be zero.
- True
- False
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Consider the definition of direction ratios.
Question 5.
Determine the symmetric form of a line through points A(2,3,5) and B(5,6,8).
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Use the concept of direction ratios and the coordinates of the given points.
Question 6.
Given the symmetric form $\frac{x - 4}{a} = \frac{y + 5}{b} = \frac{z - 6}{c}$ , if a = 0, what does this line represent?
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Think about what it means to not have a directional change in one axis.

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