Three Dimensional Geometry - Direction Cosines/Ratios

Grade 12 Maths Higher — Three Dimensional Geometry - Direction Cosines/Ratios: 25 practice questions with instant scoring and explanations.

1. Direction cosines (l, m, n) satisfy:
2. Direction cosines are related to direction ratios (a, b, c) by:
3. If direction ratios are (1, 2, 2), then r =
4. Direction cosines for ratios (1, 2, 2) are:
5. For a line with direction cosines (l, m, n), l² + m² + n² =
6. The angle θ between two lines with direction cosines (l₁, m₁, n₁) and (l₂, m₂, n₂) is:
7. If two lines have the same direction cosines:
8. Lines are perpendicular if l₁l₂ + m₁m₂ + n₁n₂ =
9. Direction cosines of z-axis are:
10. For line joining (1, 2, 3) and (4, 5, 6):
11. If direction ratios are (0, 1, 0), the line is parallel to:
12. Direction cosines for (2, -1, 2) with r = √(4+1+4) = 3:
13. Angle between lines with direction ratios (1, 1, 2) and (1, -2, 1):
14. For direction ratios (a, b, c), they are proportional to:
15. Negative direction cosines (-l, -m, -n) represent:
16. If cos(α) = l, cos(β) = m, cos(γ) = n, then α, β, γ are:
17. cos²(α) + cos²(β) + cos²(γ) =
18. For a line parallel to xy-plane, direction cosine n =
19. Angle between a line and coordinate plane is complementary to:
20. If direction ratios are (1, m, 2) and (2, 1, 3), lines perpendicular when m =
21. The angle between lines with direction cosines (1/√3, 1/√3, 1/√3) and (1/√2, 1/√2, 0) is:
22. Direction ratios determine direction uniquely up to:
23. The direction cosines (±l, ±m, ±n) represent:
24. Review question for Three Dimensional Geometry - Direction Cosines/Ratios
25. Review question for Three Dimensional Geometry - Direction Cosines/Ratios