Practice Angle Between Two Lines (6) - Three Dimensional Geometry

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8 questions

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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What are direction ratios and why are they important?
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Think about how they relate to direction cosines.
Question 2.
Use the direction ratios (1, 1, 1) and (2, 2, 2) to find the angle between the lines.
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What does it mean when ratios are proportional?
3Question 3.
What are direction ratios used for in three-dimensional geometry?
- To describe lines
- To calculate areas
- To measure distances
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Think about how they define a line's slope or direction.
4Question 4.
True or False: The angle between two lines can also be determined from their direction cosines.
- True
- False
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Relate it to how angles are calculated.
Question 5.
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).
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Form the vector, simplify the direction ratios, and apply the cosine formula.
Question 6.
Prove if the lines (3, 2, 5) and (1, -1, -1) are perpendicular by checking the angle between them.
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Focus on the numerator of the cosine formula.

4 more questions in this section. Enroll free to practise them all.