Match each item g
(a) – (iii), (b) – (i), (c) – (ii), (d) – (vi), (e) – (iv),
(f) – (v), (g) – (viii), (h) – (vii), (i) – (x), (j) – (ix)
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 1st 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.
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