Points in ℝ3 Find the coordinates of the vertices A, B, and C of the following rectangular boxes.
Given: Two points (0, 0, 10) and (5, 8, 0)
To Find: Coordinates of the vertices A, B and C
Calculations:
To find coordinates of point A
Point A and (0, 0, 10) lies in the same line and it is parallel to the x- axis
Hence, the y and z coordinates will remain same but x coordinate varies
So Point A is of form (x, 0, 10) and A is diagonally opposite to (5, 8, 10), hence x coordinate of point A is 5
So point A is (5, 0, 10)
To find coordinates of point B
Point B lies on y-axis and hence its x and z coordinates are 0
Point B is of the form (0, y, 0)
Also point B and (5, 8, 0) are on the same line and parallel to the x-axis
Hence y = 8
Point B is (0, 8, 0)
To find coordinates of point C
Point C is on the same line of point A, z coordinate of C is 10.
x-coordinate is 5
y coordinate is same as coordinate of B that is 8
Point C is (5, 8 10)
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