4 - Direction Cosines and Direction Ratios
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Practice Questions
Test your understanding with targeted questions
State the relationship between direction cosines and direction ratios.
💡 Hint: Think about how direction ratios are derived.
What is the sum of the squares of direction cosines?
💡 Hint: Recall the equation that defines the direction cosines.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What do direction cosines represent?
💡 Hint: Think about the term 'cosine' in relation to angles.
True or False: Direction ratios must always sum to one.
💡 Hint: What property is unique to direction cosines?
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Challenge Problems
Push your limits with advanced challenges
Given points A(2, 3, 4) and B(5, 6, 7), derive the direction cosines and ratios, then find the angle they create with each axis.
💡 Hint: Focus on the differences first—this will lead you to your direction cosines.
If a line has a direction ratio of (3, 4, 0), calculate the angle it makes with the X and Y axes.
💡 Hint: Remember that angles can be found with the cosine of the direction cosine values.
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