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Question

A cube of side 5 has one vertex at the point (1, 0, -1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.


Solution

Let P = (1, 0, -1) The length of each side of the cube is 5. The three edges from vertex of the cube are drawn from P towards the negative x and y axes and positive z-axis. Therefore, the coordinates of the vertex of the cube will be as follows : x-coordinate = 1,1 -5 = -4, i.e. 1, -4 y-coordinate = 0,0 -5 = -5, i.e. 0, -5 z-coordinate = -1, -1 + 5 = 4, i.e. -1, 4 Hence, the remaining seven vertices of the cube are as follows : (1, 0, 4)(1, -5, -1)(1, -5, 4)(-4, 0, -1), (-4, 0, 4) (-4, -5, -1)(-4, -5, 4)

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