Practice Equation Of A Line In Space (5) - Three Dimensional Geometry - ICSE 12 Mathematics

Practice: Equation of a Line in Space

Lesson 5Three Dimensional Geometry

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9 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Write the vector form of a line passing through point A(1, 2, 3) with direction ratios (1, 2, 3).
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Use the formula \$ \\vec{r} = \\vec{a} + \\lambda \\vec{b} \$.
Question 2.
What is the parametric equation of a line with point (0, 0, 0) and direction vector (1, 1, 1)?
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Remember to express each coordinate in terms of \$ \\lambda \$.
3Question 3.
Which form expresses a line using a direction vector?
- Parametric Form
- Symmetric Form
- Vector Form
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Think about the way each form is structured.
4Question 4.
True or False: The parametric form can be used to find specific points on the line.
- True
- False
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Recall how we use \$ \\lambda \$ in those equations.
Question 5.
Given a point A(2, 3, 4) and direction ratios (1, -1, 2), write the equations in all three forms: vector, parametric, and symmetric.
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Use the initial point and direction ratios for conversions.
Question 6.
Prove that the point (3, 4, 5) lies on the line defined by $\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-2}{3}$ .
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Verify each coordinate substitution against the symmetric definitions.

5 more questions in this section. Enroll free to practise them all.