5 - Equation of a Line in Space
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Practice Questions
Test your understanding with targeted questions
Write the vector form of a line passing through point A(1, 2, 3) with direction ratios (1, 2, 3).
💡 Hint: Use the formula \\( \\vec{r} = \\vec{a} + \\lambda \\vec{b} \\).
What is the parametric equation of a line with point (0, 0, 0) and direction vector (1, 1, 1)?
💡 Hint: Remember to express each coordinate in terms of \\( \\lambda \\).
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which form expresses a line using a direction vector?
💡 Hint: Think about the way each form is structured.
True or False: The parametric form can be used to find specific points on the line.
💡 Hint: Recall how we use \\( \\lambda \\) in those equations.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a point A(2, 3, 4) and direction ratios (1, -1, 2), write the equations in all three forms: vector, parametric, and symmetric.
💡 Hint: Use the initial point and direction ratios for conversions.
Prove that the point (3, 4, 5) lies on the line defined by \( \frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-2}{3} \).
💡 Hint: Verify each coordinate substitution against the symmetric definitions.
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