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Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.?
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Find the perpendicular distances of the point P(a,b,c) from the co-ord...
To find the perpendicular distances of the point P(a,b,c) from the coordinate axes, we can use the formulas for the distance from a point to a line in three-dimensional space.
The distance from the point P(a,b,c) to the x-axis is:
distance to x-axis = |a|
The distance from the point P(a,b,c) to the y-axis is:
distance to y-axis = |b|
The distance from the point P(a,b,c) to the z-axis is:
distance to z-axis = |c|
In each of these formulas, the absolute value (|a|, |b|, or |c|) represents the distance of the point from the corresponding axis, regardless of whether the point is above or below the axis.
For example, if the point P is (3,4,5), then the distances from P to the x-axis, y-axis, and z-axis would be 3, 4, and 5, respectively. If the point P is (-2,1,-3), then the distances from P to the x-axis, y-axis, and z-axis would be 2, 1, and 3, respectively.
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Find the perpendicular distances of the point P(a,b,c) from the co-ord...
Perpendicular Distances from the Coordinate Axes
To find the perpendicular distances of a point P(a,b,c) from the coordinate axes, we need to consider the three axes separately: the x-axis, the y-axis, and the z-axis.
Perpendicular Distance from the x-axis
The x-axis is a horizontal line passing through the origin. The perpendicular distance of a point P(a,b,c) from the x-axis is simply the vertical distance between the point and the x-axis. This distance can be found by subtracting the y-coordinate of the point from zero (since the x-axis has a y-coordinate of zero).
Perpendicular distance from the x-axis = |b - 0| = |b|
Perpendicular Distance from the y-axis
The y-axis is a vertical line passing through the origin. The perpendicular distance of a point P(a,b,c) from the y-axis is the horizontal distance between the point and the y-axis. This distance can be found by subtracting the x-coordinate of the point from zero (since the y-axis has an x-coordinate of zero).
Perpendicular distance from the y-axis = |a - 0| = |a|
Perpendicular Distance from the z-axis
The z-axis is a vertical line passing through the origin. The perpendicular distance of a point P(a,b,c) from the z-axis is the horizontal distance between the point and the z-axis. This distance can be found by subtracting the x-coordinate of the point from zero (since the z-axis has an x-coordinate of zero).
Perpendicular distance from the z-axis = |c - 0| = |c|
Summary
To summarize, the perpendicular distances of a point P(a,b,c) from the coordinate axes are:
- Perpendicular distance from the x-axis: |b|
- Perpendicular distance from the y-axis: |a|
- Perpendicular distance from the z-axis: |c|
These distances represent the shortest distances between the point and the respective axes.
To find the perpendicular distances of a point P(a,b,c) from the coordinate axes, we need to consider the three axes separately: the x-axis, the y-axis, and the z-axis.
Perpendicular Distance from the x-axis
The x-axis is a horizontal line passing through the origin. The perpendicular distance of a point P(a,b,c) from the x-axis is simply the vertical distance between the point and the x-axis. This distance can be found by subtracting the y-coordinate of the point from zero (since the x-axis has a y-coordinate of zero).
Perpendicular distance from the x-axis = |b - 0| = |b|
Perpendicular Distance from the y-axis
The y-axis is a vertical line passing through the origin. The perpendicular distance of a point P(a,b,c) from the y-axis is the horizontal distance between the point and the y-axis. This distance can be found by subtracting the x-coordinate of the point from zero (since the y-axis has an x-coordinate of zero).
Perpendicular distance from the y-axis = |a - 0| = |a|
Perpendicular Distance from the z-axis
The z-axis is a vertical line passing through the origin. The perpendicular distance of a point P(a,b,c) from the z-axis is the horizontal distance between the point and the z-axis. This distance can be found by subtracting the x-coordinate of the point from zero (since the z-axis has an x-coordinate of zero).
Perpendicular distance from the z-axis = |c - 0| = |c|
Summary
To summarize, the perpendicular distances of a point P(a,b,c) from the coordinate axes are:
- Perpendicular distance from the x-axis: |b|
- Perpendicular distance from the y-axis: |a|
- Perpendicular distance from the z-axis: |c|
These distances represent the shortest distances between the point and the respective axes.
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Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.?
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Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.?.
Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the perpendicular distances of the point P(a,b,c) from the co-ordinate axes.?.
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