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Three-Dimensional Geometry

Mathematics · Class 12 · All

MathematicsClass 12AllEasy
Q1/15
45s

The direction ratios of the line joining the points A(1, 2, 3) and B(5, 7, 9) are

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All 15 questions in this quiz

  1. Which of the following statements is true regarding Three Dimensional Geometry?

    1. Every point is represented by only two coordinates.
    2. Every point in space is represented by three coordinates.
    3. Three-dimensional geometry deals only with planes.
    4. Distance cannot be calculated between two points.

  2. If the direction cosines of a line are (l, m, n), then the corresponding unit vector along the line is

    1. li + mj + nk
    2. il + jm + kn + 1
    3. li + mj
    4. l + m + n

  3. The angle between two parallel lines is

    1. 30 degrees
    2. 45 degrees
    3. 0 degrees
    4. 90 degrees

  4. If the direction ratios of two lines are proportional, then the lines are

    1. Perpendicular
    2. Parallel
    3. Intersecting at right angles
    4. Coincident in every case

  5. The line (x - 2)/3 = (y + 1)/4 = (z - 5)/(-2) passes through the point

    1. (2, -1, 5)
    2. (3, 4, -2)
    3. (-2, 1, -5)
    4. (2, 1, 5)

  6. The distance between the points (2, -1, 5) and (2, -1, 9) is

    1. 2
    2. 3
    3. 4
    4. 5

  7. The direction ratios of a line parallel to the vector 4i - 2j + 6k are

    1. (4, -2, 6)
    2. (2, 1, 3)
    3. (-4, 2, -6)
    4. All of these

  8. The direction cosines corresponding to the direction ratios (2, 3, 6) are

    1. (2/7, 3/7, 6/7)
    2. (2, 3, 6)
    3. (1/2, 1/3, 1/6)
    4. (2/6, 3/6, 6/6)

  9. The angle between two lines is determined using their

    1. Midpoints
    2. Direction ratios or direction cosines
    3. End points only
    4. Distances from the origin

  10. The Cartesian equation of the line passing through the point (1, 2, 3) and having direction ratios (2, -1, 4) is

    1. (x - 1)/2 = (y - 2)/(-1) = (z - 3)/4
    2. (x + 1)/2 = (y + 2)/(-1) = (z + 3)/4
    3. (x - 2)/1 = (y - 1)/2 = (z - 4)/3
    4. x/2 = y/(-1) = z/4

  11. The vector equation of a line passing through the point with position vector a and parallel to vector b is

    1. r = a + λb
    2. r = a − λb only
    3. r = λa + b
    4. r = a × b

  12. The direction cosines of a line satisfy

    1. l + m + n = 1
    2. l^2 + m^2 + n^2 = 1
    3. lmn = 1
    4. l = m = n

  13. The direction ratios of the line joining the points A(1, 2, 3) and B(5, 7, 9) are

    1. (4, 5, 6)
    2. (5, 7, 9)
    3. (1, 2, 3)
    4. (6, 9, 12)

  14. The coordinates of the midpoint of the line segment joining A(2, 4, 6) and B(6, 8, 10) are

    1. (4, 6, 8)
    2. (8, 12, 16)
    3. (2, 2, 2)
    4. (3, 5, 7)

  15. The distance between the points A(1, 2, 3) and B(4, 6, 3) is

    1. 3
    2. 4
    3. 5
    4. 7