Draw a right -handed rectangular reference frame with axes ranges x = -5 to +5, y = -5 to +10 , z = -5 to +5. Sketch the following planes on your reference frame. X-y plane passing through z =5, y-z plane passing through x = -2, z-x plane passing through y =8. What are the cartesian co ordinates of the point at which the three planes all meet?
since you have only provided a single value for each coordinate, and the planes are all perpendicular to an axis, the intersection must clearly be (-2,8,5).
To draw the right-handed rectangular reference frame with the given axes ranges, follow these steps:
1. Draw three perpendicular lines intersecting at a point. This point will be the origin of the reference frame.
2. Label the three lines as x, y, and z, corresponding to the x-axis, y-axis, and z-axis, respectively.
3. Measure a distance of 10 units above the origin on the y-axis and mark it. Similarly, measure a distance of 5 units in both the positive and negative directions on the x-axis and z-axis, and mark them.
4. Connect the marked points on the x-axis, y-axis, and z-axis to form the three rectangular axes.
Now, let's sketch the three given planes on the reference frame:
1. X-y plane passing through z = 5:
- Draw a horizontal plane parallel to the x-y plane, crossing the z-axis at z = 5.
- Extend the plane across the x and y axes.
2. Y-z plane passing through x = -2:
- Draw a vertical plane parallel to the y-z plane, crossing the x-axis at x = -2.
- Extend the plane across the y and z axes.
3. Z-x plane passing through y = 8:
- Draw a vertical plane parallel to the z-x plane, crossing the y-axis at y = 8.
- Extend the plane across the z and x axes.
To find the Cartesian coordinates of the point at which the three planes meet:
1. Locate the point where the three planes intersect on the reference frame.
2. Read the coordinates on each axis at the intersection point to determine the Cartesian coordinates of the point.
Please note that without precise measurements on the reference frame, it is difficult to determine the exact Cartesian coordinates of the point where the three planes intersect.