Practice Equation of a Line in 3D - 5 | 7. 3D Geometry | (IB) Class 10 Mathematics – Group 5, Geometry & Trigonometry
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5 - Equation of a Line in 3D

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What are the parametric equations of a line through point A(0, 0, 0) with direction vector (1, 1, 1)?

💡 Hint: Remember to express each coordinate with respect to the parameter 't'.

Question 2

Easy

What is the symmetric form for the line defined by the parametric equations x = 2 + 3t, y = 5 + 6t, z = 7 + 8t?

💡 Hint: Convert each equation back to express the ratio.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the first step to write the parametric form of a line?

💡 Hint: Think about what you need to define a path in space.

Question 2

True or False: The symmetric form can be used when any part of the direction vector is zero.

  • True
  • False

💡 Hint: Consider the implications of zero in ratios.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given two points F(1, 2, 3) and G(-1, -2, -4), write the line equation in both parametric and symmetric forms and explain any assumptions if one direction vector component is zero.

💡 Hint: Remember, how does zero in a vector change the representation?

Question 2

Find the distance between two lines defined by their equations: L1: (x - 2)/1 = (y - 3)/2 and L2: (x - 4)/-1 = (y + 1)/3. Are they parallel?

💡 Hint: What defines parallelism in lines?

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