6 - Angle Between Two Lines
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Practice Questions
Test your understanding with targeted questions
What are direction ratios and why are they important?
💡 Hint: Think about how they relate to direction cosines.
Use the direction ratios (1, 1, 1) and (2, 2, 2) to find the angle between the lines.
💡 Hint: What does it mean when ratios are proportional?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What are direction ratios used for in three-dimensional geometry?
💡 Hint: Think about how they define a line's slope or direction.
True or False: The angle between two lines can also be determined from their direction cosines.
💡 Hint: Relate it to how angles are calculated.
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Challenge Problems
Push your limits with advanced challenges
Calculate the angle between the line passing through the points (1, 2, 3) and (2, 3, 4) with the line represented by direction ratios (4, 0, -4).
💡 Hint: Form the vector, simplify the direction ratios, and apply the cosine formula.
Prove if the lines (3, 2, 5) and (1, -1, -1) are perpendicular by checking the angle between them.
💡 Hint: Focus on the numerator of the cosine formula.
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