Practice Direction Cosines and Direction Ratios - 4 | 6. Three Dimensional Geometry | ICSE 12 Mathematics
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Direction Cosines and Direction Ratios

4 - Direction Cosines and Direction Ratios

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

State the relationship between direction cosines and direction ratios.

💡 Hint: Think about how direction ratios are derived.

Question 2 Easy

What is the sum of the squares of direction cosines?

💡 Hint: Recall the equation that defines the direction cosines.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What do direction cosines represent?

Angles a line makes with axes
Length of a line
Direction ratios

💡 Hint: Think about the term 'cosine' in relation to angles.

Question 2

True or False: Direction ratios must always sum to one.

True
False

💡 Hint: What property is unique to direction cosines?

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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Reference links

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