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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.


A
(1,0,1)
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B
(0,-1,0)
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C
(0,0,-1)
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D
(1,0,0)
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Solution

The correct option is B  (0,-1,0)
Consider the problem 
Below, are four complete cube face on $$XZ-plane,\,(y=0)$$  

Given point
$$(1,0,-1)$$

End of the edge parallel to negative $$x-axis$$ 
$$(0,0-1)$$

Origin 
$$(0,0,0)$$

End of the edge parallel to positive $$z-axis $$
$$(1,0,0)$$

And, below 
Four point complete the opposite face of cube. 

consider $$P$$, end of edge parallel to negative  $$y-axis $$
$$(1,-1,-1)$$

Edge from $$P$$ parallel to positive $$z-axis $$
$$(0,-1,0)$$

Edge from $$P$$ parallel to negative $$x-axis $$
$$(0,-1,-1)$$

And 
$$(0,-1,0)$$

Mathematics

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