The Three coordinate planes divide the whole space into how many octants?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Explanation:

The three coordinate planes divide the whole space into Eight Parts, called octants. These eight octants and signs of the co-ordinates of a point P in each one of them are shown below :

Remark : Three fixed lines X'OX Y' O Y and Z' O Z are called x, y and z-axis respectively and their common point of intersection ‘O' is called the origin or pole of coordinates.

Dividing the Space:

The three coordinate planes divide the space into eight octants as follows:

1. First Octant: This octant is located in the positive region of all three coordinate planes, where x, y, and z are all positive.

2. Second Octant: This octant is located in the negative region of the x-axis, positive region of the y-axis, and positive region of the z-axis, where x is negative, y is positive, and z is positive.

3. Third Octant: This octant is located in the negative region of the x-axis, negative region of the y-axis, and positive region of the z-axis, where x is negative, y is negative, and z is positive.

4. Fourth Octant: This octant is located in the positive region of the x-axis, negative region of the y-axis, and positive region of the z-axis, where x is positive, y is negative, and z is positive.

5. Fifth Octant: This octant is located in the positive region of the x-axis, positive region of the y-axis, and negative region of the z-axis, where x is positive, y is positive, and z is negative.

6. Sixth Octant: This octant is located in the negative region of the x-axis, positive region of the y-axis, and negative region of the z-axis, where x is negative, y is positive, and z is negative.

7. Seventh Octant: This octant is located in the negative region of the x-axis, negative region of the y-axis, and negative region of the z-axis, where x is negative, y is negative, and z is negative.

8. Eighth Octant: This octant is located in the positive region of the x-axis, negative region of the y-axis, and negative region of the z-axis, where x is positive, y is negative, and z is negative.

Number of Octants:

Therefore, the three coordinate planes divide the whole space into eight octants. Hence, the correct answer is option 'C', which represents 8 octants.

Answer

The three coordinate planes divide the whole space into Eight Parts, called octants. These eight octants and signs of the co-ordinates of a point P in each one of them are shown below :

Remark : Three fixed lines X'OX Y' O Y and Z' O Z are called x, y and z-axis respectively and their common point of intersection ‘O' is called the origin or pole of coordinates.

Answer

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