Practice Vector Form - 5.1 | 6. Three Dimensional Geometry | ICSE Class 12 Mathematics
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5.1 - Vector Form

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Write the vector equation of a line passing through the point (3, 2, 1) with direction vector (2, 1, 0).

💡 Hint: Use the provided point as your position vector and the direction vector directly.

Question 2

Easy

What does the scalar 'λ' represent in the vector equation of a line?

💡 Hint: Think about how you can move away from the position vector.

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 does the vector form of a line in 3D express?

  • Only the direction
  • A single point
  • A set of points along a line

💡 Hint: Think about how the variable changes the positioning.

Question 2

In the vector equation r⃗ = a⃗ + λb⃗, which vector represents the starting point?

  • a⃗
  • b⃗
  • λ

💡 Hint: Recall which part serves as the reference point.

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Challenge Problems

Push your limits with challenges.

Question 1

Two points A(1, 2, 3) and B(4, 5, 6) define a line. Write the vector form, parametric, and symmetric forms of the line.

💡 Hint: Calculate the direction vector and begin forming representations.

Question 2

For the line defined by r⃗ = (2, 3, 4) + λ(1, -1, 0). If λ = 3, find the coordinates of the corresponding point on the line.

💡 Hint: Substitute λ into the parametric equations derived from the vector form.

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