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Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the space into eight parts. Each part is called an OCTANT. What is the relation between these three planes
- a)They form the angles α, β & γ with each other
- b)Any two must be perpendicular to each other.
- c)All three are mutually perpendicular
- d)no relation between these three planes
Correct answer is option 'C'. Can you explain this answer?
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Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the s...
The three mutually perpendicular coordinate planes which in turn divide the space into eight parts and each part is known as octant.
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Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the s...
Understanding the Relation Between the Planes
The XY, XZ, and YZ planes are fundamental to the three-dimensional Cartesian coordinate system. Their relationship is defined by the angles and orientations they form with each other.
Perpendicular Planes
- The XY Plane is defined by the equation z = 0, where the x and y coordinates vary freely while z remains constant.
- The XZ Plane is defined by the equation y = 0, where x and z vary freely while y remains constant.
- The YZ Plane is defined by the equation x = 0, where y and z vary freely while x remains constant.
Mutual Perpendicularity
- Each of these planes intersects the others at right angles, which means they are mutually perpendicular.
- For example, the intersection of the XY Plane and XZ Plane occurs along the x-axis, and both planes meet at a 90-degree angle.
Conclusion
- Because all three planes intersect each other at right angles, the correct relationship among them is that they are mutually perpendicular.
- This property of mutual perpendicularity is fundamental in defining the octants in space, as they create distinct regions that divide the space into eight parts.
In summary, the correct answer is option 'C', indicating that all three planes are mutually perpendicular to each other, forming the basis for the 3D Cartesian coordinate system and creating the octants.
The XY, XZ, and YZ planes are fundamental to the three-dimensional Cartesian coordinate system. Their relationship is defined by the angles and orientations they form with each other.
Perpendicular Planes
- The XY Plane is defined by the equation z = 0, where the x and y coordinates vary freely while z remains constant.
- The XZ Plane is defined by the equation y = 0, where x and z vary freely while y remains constant.
- The YZ Plane is defined by the equation x = 0, where y and z vary freely while x remains constant.
Mutual Perpendicularity
- Each of these planes intersects the others at right angles, which means they are mutually perpendicular.
- For example, the intersection of the XY Plane and XZ Plane occurs along the x-axis, and both planes meet at a 90-degree angle.
Conclusion
- Because all three planes intersect each other at right angles, the correct relationship among them is that they are mutually perpendicular.
- This property of mutual perpendicularity is fundamental in defining the octants in space, as they create distinct regions that divide the space into eight parts.
In summary, the correct answer is option 'C', indicating that all three planes are mutually perpendicular to each other, forming the basis for the 3D Cartesian coordinate system and creating the octants.
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Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the space into eight parts. Each part is called an OCTANT. What is the relation between these three planesa)They form the angles α, β & γ with each otherb)Any two must be perpendicular to each other.c)All three are mutually perpendiculard)no relation between these three planesCorrect answer is option 'C'. Can you explain this answer?
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