First slide
Introduction to 3-D Geometry
Question

The projections of the line segment AB¯ on the axes are 5,12,7. Then the length of AB¯ is 

Very Easy
Solution

If d1,d2,d3 are the projections of the line segment of length d on the coordinate axes then d12+d22+d32=d2

It implies that 52+122+72=d225+144+49=d2d=218

Therefore,d=21092

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