Question types

Introduction to Three Dimensional Geometry question types

50 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

50
Questions
6
Question groups
5
Question types
Sample Questions

Introduction to Three Dimensional Geometry questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

What is the length of foot of perpendicular drawn from the point $P(3, 4, 5)$ on $y-$axis.
  • A
    $\sqrt{41}$
  • $\sqrt{34}$
  • C
    $5$
  • D
    $\text{None of these.}$

Answer: B.

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$L$ is the foot of the perpendicular drawn from a point $P(3, 4, 5)$ on the $xy-$plane. The coordinates of point $L$ are:
  • A
    $(3, 0, 0).$
  • B
    $(0, 4, 5).$
  • C
    $(3, 0, 5).$
  • None of these.

Answer: D.

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If a parallelopiped is formed by planes drawn through the points $(5, 8, 10)$ and $(3, 6, 8)$ parallel to the coordinate planes, then the length of diagonal of the parallelopiped is:
  • $2\sqrt{3}$
  • B
    $3\sqrt{2}$
  • C
    $\sqrt{2}$
  • D
    $\sqrt{3}$

Answer: A.

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Show that if $\text{x}^2 + \text{y}^2 = 1,$ then the point $\Big(\text{x, y},\sqrt{1-\text{x}^2-\text{y}^2}\Big)$ is at a distance 1 unit from the origin.
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What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the three edges passing through the origin, coincides with the positive direction of the axes through the origin?
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Q 133 Marks Question3 Marks
Let $A, B, C$ be the feet of perpendiculars from a point $P$ on the $x, y, z-$axis respectively. Find the coordinates of $A, B$ and $C$ in each of the following where the point $P$ is:
  1. $A(3, 4, 2).$
  2. $B(-5, 3, 7).$
  3. $C(4, -3, -5).$
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Q 143 Marks Question3 Marks
Prove that the points (0, -1, -7), (2, 1, -9) and (6, 5, -13) are collinear. Find the ratio in which the first point divides the join of the other two.
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Match each item given under the column $C_1$ to its correct answer given under column $C_2$.
  Column $C_1$   Column $C_2$
$a.$ In $xy-$plane. $i.$ $I^{st}$ octant.
$b.$ Point $(2, 3, 4)$ lies in the. $ii.$ $yz-$plane.
$c.$ Locus of the points having $x$ coordinate $0$ is. $iii.$ $z-$coordinate is zero.
$d.$ $A$ line is parallel to $x-$axis if and only. $iv.$ $z-$axis.
$e.$ If $x = 0, y = 0$ taken together will represent the. $v.$ plane parallel to $xy-$plane.
$f.$ $z = c$ represent the plane. $vi.$ if all the points on the line have equal $y$ and $z-$coordinates.
$g.$ Planes $x = a, y = b$ represent the line. $vii.$ from the point on the respective.
$h.$ Coordinates of a point are the distances from the origin to the feet of perpendiculars. $viii.$ parallel to $z-$axis.
$i.$ A ball is the solid region in the space enclosed by a. $ix$ disc.
$j.$ Region in the plane enclosed by a circle is known as a. $x.$ sphere.
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The mid$-$point of the sides of a triangle are $(1, 5, -1), (0, 4, -2)$ and $(2, 3, 4)$. Find its vertices. Also find the centriod of the triangle.
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Name the octant in which each of the following points lies:
  1. $(1, 2, 3).$
  2. $(4, -2, 3).$
  3. $(4, -2, -5).$
  4. $(4, 2, -5).$
  5. $(-4, 2, 5).$
  6. $(-3, -1, 6).$
  7. $(2, -4, -7).$
  8. $(-4, 2, -5).$
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