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Introduction to Three Dimensional Geometry — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsIntroduction to Three Dimensional Geometry5 Marks
Question
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.
✓

Answer

  Column $C_1$   Column $C_2$
$a.$ In $xy-$plane. $iii.$ $z-$coordinate is zero.
$b.$ Point $(2, 3, 4)$ lies in the. $i.$ $1^{st}$ octant.
$c.$ Locus of the points having $x$ coordinate $0$ is. $ii.$ $yz-$plane.
$d.$ $A$ line is parallel to $x-$axis if and only. $vi.$ If all the points on the line have equal $y$ and $z-$coordinates.
$e.$ If $x = 0, y = 0$ taken together will represent the. $iv.$ $z-$axis.
$f.$ $z = c $represent the plane. $v.$ Plane parallel to $xy-$plane.
$g.$ Planes $x = a, y = b$ represent the line. $viii.$ Parallel to $z-$axis.
$h.$ Coordinates of a point are the distances from the origin to the feet of perpendiculars. $vii.$ From the point on the respective.
$i.$ $A$ ball is the solid region in the space enclosed by a. $x$ Sphere.
$j.$ Region in the plane enclosed by a circle is known as a. $ix.$ Disc.
  1. In $xy-$plane, $z-$coordinate is zero.
  2. The point $(2, 3, 4)$ lies in $1^{st}$ octant.
  3. Locus of the points having $x-$coordinate zero is $yz-$plane.
  4. $A$ line is parallel to $x-$axis if and only if all the points on the line have equal $y$ and $z-$coordinates.
  5. $x = 0, y = 0$ represent $z-$axis
  6. $z = c$ represents the plane parallel to $xy-$plane.
  1. The plane $x = a$ is parallel to $yz-$plane.
Plane $y = b$ is parallel to $xz-$plane.
So, planes $x = a$ and $y = b$ is line of intersection of these planes.
Now, line of intersection of $yz-$plane and $xz-$plane is $z-$axis.
So, line of intersection of planes $x = a$ andy $= b$ is line parallel to $z-$axis.
  1. Coordinates of a point are the distances from the origin to the feet of perpendicular from the point on the respective axis.
  2. A ball is the solid region in the space enclosed by a sphere.
  3. The region in the plane enclosed by a circle is known as a disc.

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