Question

A cuboid is drawn in 3-D space. Length, width and height of the cuboid is 3, 2 and 1 unit respectively. X, Y and Z axes are given with one of the corners as the origin.

How many of the following coordinates are correct?

A (0, 1, 0)

B (3, 0, 1)

C (3, 0, 0)

D (2, 3, 0)

E (1, 2, 3)

F (0, 2, 0)

G (0, 2, 1)

H (0, 0, 0)

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Answer 1

For a given point P in a space, we drop a perpendicular PM on the xz plane with M as a foot of perpendicular, then from the point M, we draw a perpendicular ML to the z-axis meeting it at the L. let OL be z, LM be x and MP be y. x, y and z are called the x, y and z coordinates respectively of the point P in the space. Coordinate of the point P are (x, y, z)

We will use the same concept to proceed.

Coordinates of point A

Point A lies on the z axis $\Rightarrow$ x & y coordinates must be zero.

z- coordinate is 1. Coordinates of point A are (0, 0, 1)

Coordinate of point B

Point B lies on the x – z plane, y-coordinates must be zero and the value of x and z- coordinate is 3 and 1.Coordinate of point B are (3, 0, 1)

Coordinate of point C

Point C lies on the x-axis $\Rightarrow$ y & z coordinate must be zero.

x coordinate is 3. Coordinate of point C are (3, 0, 0).

Coordinate of Point D

Point D lies on the x – y, plane, z-coordinate must be zero and the value of x and y- coordinate is 3 and 2. Coordinate of point D are (3, 2, 0).

Coordinates of point E

To reach E, we travel 3 units in the positive x direction and 2 and 1 units in the positive y and z direction. So the Coordinates of Point E will be (3, 2, 1).

Similarly, we get the coordinates of F and G equal to (0,2,0) and (0,2,1).

Coordinates of point H is (0, 0, 0) since it is the origin.

So, only 5 coordinates are correct.