Introduction to Three Dimensional Geometry MATHS - Introduction to Three Dimensional Geometry

Equation of y-axis is considered as:

1. x = 0, y = 0.
2. y = 0, z = 0.
3. z = 0, x = 0.
4. None of these.

A plane is parallel to yz-plane so it is perpendicular to:

1. x-axis.
2. y-axis.
3. z-axis.
4. None of these.

The distance of point P(3, 4, 5) from the yz-plane is:

1. 3 units.
2. 4 units.
3. 5 units.
4. 550.

The point (-2, -3, -4) lies in the:

1. First octant.
2. Seventh octant.
3. Second octant.
4. Eighth octant.

x = a represent a plane parallel to ________.

The plane parallel to yz-plane is perpendicular to ________.

The length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 10, 13 and 8 units are ______.

A line is parallel to x-axis if all the points on the line have equal ________.

The three coordinate planes divide the space into ________ parts.

How far apart are the points (2, 0, 0) and (-3, 0, 0)?

Find the centroid of a triangle, the mid-point of whose sides are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4).

Find the distance from the origin to (6, 6, 7).

If the origin is the centriod of a triangle ABC having vertices A(a, 1, 3), B(-2, b, -5) and C(4, 7, c), find the values of a, b, c.

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?

Locate the following points:

1. (1, -1, 3).
2. (-1, 2, 4).
3. (-2, -4, -7).
4. (-4, 2, -5).

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.

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).

Find the coordinate of the points which trisect the line segment joining the points A(2, 1, -3) and B(5, -8, 3).

Let A, B, C be the feet of perpendiculars from a point P on the xy, yz and zx-planes respectively. Find the coordinates of A, B, C in each of the following where the point P is:

1. (3, 4, 5).
2. (-5, 3, 7).
3. (4, -3, -5).

Three consecutive vertices of a parallelogram ABCD are A(6, -2, 4), B(2, 4, -8), C(-2, 2, 4). Find the coordinates of the fourth vertex.
[Hint: Diagonals of a parallelogram have the same mid-point.]

Three vertices of a Parallelogram ABCD are A(1, 2, 3), B(-1, -2, -1) and C(2, 3, 2). Find the fourth vertex D.

The mid-points of the sides of a triangle are (5, 7, 11), (0, 8, 5) and (2, 3, -1). Find its vertices.

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

	Column C1		Column C2
a.	In xy-plane.	i.	Ist 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.

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).

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.