## Maths Chapter 11 – Three-dimensional Geometry MCQ Question Answers for Various Entrance Exams

1. Question
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2. The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0
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3. Question
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4. The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
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5. Question
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6. The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are
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9. Question
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10. The plane x + y = 0
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11.  How many lines through the origin make equal angles with the coordinate axis?
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12. The direction cosines of the y-axis are:
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13. Find the equation of the plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).
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15. The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are:
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16. Question
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17. Question
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18. The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:
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19. Question
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20. The equation of the plane through the point (0, -4, -6) and (-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is
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21. Question
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22. Question
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23. The direction cosines of any normal to the xy plane are
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24. Question
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25. The acute angle between the planes 2x – y+z = 6 and x+y+2z = 3 is
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26. The equations of y-axis in space are
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27. If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is
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28. Question
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29. If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =
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30. Question
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31. Question
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32. A line makes angle α, β, γ with x-axis, y-axis and z-axis respectively then cos 2α + cos 2β + cos 2γ is equal to
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33. Question
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34. The line x = 1, y = 2 is
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35. The equation xy = 0 in three dimensional space is represented by
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36. Question
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37. The locus of xy + yz = 0 is
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39. Question
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40. Question
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41. Find the equation of plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).
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42. Question
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43. The vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is:
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44. Question
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45. The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are
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46. Question
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47. The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by
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48. The reflection of the point (a, β, γ) in the xy-plane is
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49. Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are:
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50. Question
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