Q.A point R with x-coordinate 4 lies on the line joining the points P(2, -3, 4) and Q(8, 0, 10). Find the ratio PR : RQ and the coordinates of R. OR Find the area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the end of the latus rectum.

Showing the 12 most recent of 26 on this concept.

1. CBSE 2026Set ANNUAL1 markMCQ
   Q.Distance between the points $P(1, -3, 4)$ and $Q(-4, 1, 2)$ is

   (a) $5\sqrt{3}$ unit

   (b) 7 unit

   (c) $3\sqrt{5}$ unit

   (d) 5 unit

   ›Reveal solutionSolution

   Use the 3D distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$.

   …

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2. CBSE 2026Set ANNUAL1 mark
   Q.Write True/False: The distance between points $(1, 0, 0)$ and $(0, 1, 0)$ is $\sqrt{2}$.

   ›Reveal solutionSolution

   Using the 3D distance formula, the distance between $(1,0,0)$ and $(0,1,0)$ works out to exactly $\sqrt{2}$, confirming the statement.

   Distance between $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$.

   …

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3. CBSE 2026Set ANNUAL1 mark
   Q.Find distance between the points $(4, 0, 0)$ and $(-4, 0, 0)$.

   ›Reveal solutionSolution

   Distance formula in 3D gives $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$; here it simplifies to 8, the direct separation along the x-axis.

   Points: $(4,0,0)$ and $(-4,0,0)$.

   …

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4. CBSE 2026Set 1A1 markMCQ
   Q.XOZ-plane divides the line joining the points $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio -

   (1) $3 : 7$

   (2) $2 : 7$

   (3) $-3 : 7$

   (4) $-2 : 4$

   ›Reveal solutionSolution

   Setting the $y$-coordinate to $0$ in the section formula gives ratio $-3:7$.

   Let the XOZ-plane (equation $y=0$) divide the join of $(2,3,1)$ and $(6,7,1)$ in the ratio $k:1$. The $y$-coordinate of the division point is …

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5. CBSE 2025Set ANNUAL1 markMCQ
   Q.The coordinates of origin in three dimensional geometry are

   (a) $(0, 0)$

   (b) $(0, 0, 0)$

   (c) $(0, 0, 0, 0)$

   (d) $(0, 0, 0, 0, 0)$

   ›Reveal solutionSolution

   The origin in 3D geometry is $(0,0,0)$.

   In 3D space, every point needs three coordinates (along the $x$, $y$, $z$ axes) to be located. The origin $O$ is the common point where all three coor …

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6. CBSE 2025Set ANNUAL1 markMCQ
   Q.The distance between the points $(2, 3, 5)$ and $(4, 3, 1)$ is

   (a) $\sqrt{5}$

   (b) $2\sqrt{5}$

   (c) $3\sqrt{5}$

   (d) 5

   ›Reveal solutionSolution

   Distance between $(2,3,5)$ and $(4,3,1)$ is $2\sqrt5$.

   Using the distance formula: …

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7. CBSE 2025Set ANNUAL1 markMCQ
   Q.The coordinates of the mid-point of the line joining the points $(4, 6, 8)$ and $(-8, -6, -4)$ are

   (a) $(0, 0, 0)$

   (b) $(-2, 0, 2)$

   (c) $(2, 0, -2)$

   (d) $(2, 0, 2)$

   ›Reveal solutionSolution

   Midpoint of $(4,6,8)$ and $(-8,-6,-4)$ is $(-2,0,2)$.

   Midpoint formula: $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2},\dfrac{z_1+z_2}{2}\right)$.

   …

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8. CBSE 2025Set ANNUAL1 markMCQ
   Q.The distance between the points $A(-2, 1, -3)$ and $B(4, 3, -6)$ is

   (a) 0 units

   (b) 4 units

   (c) 7 units

   (d) 12 units

   ›Reveal solutionSolution

   Apply the 3D distance formula directly to $A(-2,1,-3)$ and $B(4,3,-6)$.

   …

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9. CBSE 2025Set ANNUAL1 mark
   Q.Fill in the blank: A point with co-ordinates $(2, 3, 0)$ lies in the ____ plane.

   ›Reveal solutionSolution

   Any point of the form $(x, y, 0)$, with $z$-coordinate zero, lies in the $xy$-plane.

   In three-dimensional geometry, the $xy$-plane consists of all points whose $z$-coordinate is $0$; the $yz$-plane consists of points whose $x$-coordinate is $0$; the $xz$-plane consists of points whose $y$-coordinate is …

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10. CBSE 2025Set ANNUAL1 markMCQ
    Q.Match the column: Column A entry 'Distance of the point $(2, 4, 5)$ from the $xz$ plane' — find the matching value from Column B.

    (a) 2

    (b) 8

    (c) $\dfrac{2}{3}$

    (d) $\dfrac{2\tan x}{1 - \tan^2 x}$

    (e) $\sin 2x$

    (f) 10

    (g) 20

    (h) $\dfrac{2\tan x}{1 + \tan^2 x}$

    (i) 4

    ›Reveal solutionSolution

    The distance of any point $(x, y, z)$ from the $xz$-plane equals $|y|$; here $y = 4$.

    The $xz$-plane consists of all points with $y = 0$. The perpendicular distance of a point $(x, y, z)$ from the $xz$-plane is $|y|$.

    …

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11. CBSE 2025Set ANNUAL1 mark
    Q.A point lies in the $xz$ plane. What will be its $y$-coordinate?

    ›Reveal solutionSolution

    The $xz$-plane is defined as the set of all points with $y = 0$.

    In 3D coordinate geometry, the $xz$-plane consists of all points of the form $(x, 0, z)$ — i.e. every point on this plane has $y$-coor …

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12. CBSE 2024Set ANNUAL1 markMCQ
    Q.The distance of the point $(1,-3,4)$ from $x$-axis is

    (a) 5

    (b) 1

    (c) $\sqrt{26}$

    (d) None of these

    ›Reveal solutionSolution

    The distance from a point to the $x$-axis depends only on its $y$ and $z$ coordinates (the $x$-coordinate doesn't matter, since the foot of the perpendicular slides along the axis).

    For a point $(x, y, z)$, its perpendicular distance from the $x$-axis is:

    $d = \sqrt{y^2 + z^2}$

    …

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