First slide

Introduction to 3-D Geometry

Question

If the projections of a line of length $d$ on the coordinate axes are $d_{1}, d_{2}, d_{3}$ respectively, then ${d_{1}}^{2} + {d_{2}}^{2} + {d_{3}}^{2} - d^{2} =$

Moderate

A

$d^{2}$
B

1
C

0
D

None

Solution

If $d_{1}, d_{2}, d_{3}$ are the projections of a line segment of length $d$ on the coordinate axes then $d^{2} = {d_{1}}^{2} + {d_{2}}^{2} + {d_{3}}^{2}$
Therefore, ${d_{1}}^{2} + {d_{2}}^{2} + {d_{3}}^{2} - d^{2} = 0$

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