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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.
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Solution
Let P \[\equiv\](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 yaxes and the 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\[-\]1, 4
Hence, the remaining seven vertices of the cube are as follows:
\[\left( 1, 0, 4 \right)\]
\[\left( 1, - 5, - 1 \right)\]
\[\left( 1, - 5, 4 \right)\]
\[\left( - 4, 0, - 1 \right)\]
\[\left( - 4, 0, 4 \right)\]
\[\left( - 4, - 5, - 1 \right)\]
\[\left( - 4, - 5, 4 \right)\]
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