Match each item given under the column C₁ to its correct answer given under column C₂.

Column C₁

(a) In xy-plane

(b) Point (2, 3,4) lies in the

(c) Locus of the points having x coordinate 0 is

(d) A line is parallel to x-axis if and only

(e) If x = 0, y = 0 taken together will represent the

(f) z = c represent the plane

(g) Planes x = a, y = b represent the line

(h) Coordinates of a point are the distances from the origin to the feet of perpendiculars

(i) A ball is the solid region in the space enclosed by a

(j) Region in the plane enclosed by a circle is known as a

Column C₂

i) Ist octant

ii) yz-plane

iii) z-coordinate is zero

iv) z-axis

v) plane parallel to xy-plane

vi) if all the points on the line have equal y and z-coordinates

vii) from the point on the respective axis

viii) parallel to z - axis.

ix) Disc

x) Sphere

(a) – (iii), (b) – (i), (c) – (ii), (d) – (vi), (e) – (iv),

(f) – (v), (g) – (viii), (h) – (vii), (i) – (x), (j) – (ix)

Explanation:

a) In xy - plane all points lie on it. So distance from xy plane remains 0.

∴ we can say that z-coordinate is 0

b) Point (2,3,4) has all coordinates positive. So it implies that the point lies in the 1^st octant.

c) If x – coordinate of a point is zero. This means that its distance from yz plane is zero or we can say that point lies on yz plane.

∴ Locus of point having x coordinate 0 is yz plane

d) For a line to be parallel to x-axis , it must remain parallel to xz and xy plane. As they remain parallel to these plane, all points on the line has a fixed or equal y and z coordinate.

e) x = 0 and y = 0 is the locus of z-axis.

∴ They represent z – axis.

f) As all points on the plane z = c has fixed z coordinate or we can say that they are at a constant distance from xy plane.

∴ z = c is a plane parallel to xy plane.

g) The plane x = a is parallel to yz-plane.

Plane y = b is parallel to xz-plane.

So, planes x = a and y = b gives the set of coordinates that satisfies both the equation of plane.

It means these points are the point of intersection of these plane and these points constitute a line called line of intersection of planes

Now, line of intersection of yz-plane and xz-plane is z-axis.

∵ x = a and y = b are planes parallel to yz and xz. So their line of intersection will be parallel to z-axis.

h) By basic definition of coordinates we know that coordinates of a point are the distances from the origin to the feet of perpendicular from the point on the respective axis.

(i) A ball is the solid region in the space enclosed by a sphere.

(j) The region in the plane enclosed by a circle is known as a disc.