First slide

Introduction to 3-D Geometry

Question

The projections of a line segment on the axes are 1,2,2. If the length of the segment is n, then $\log_{3} \sqrt{n} =$

Moderate

A

2
B

0.2
C

0.5
D

5

Solution

If the projections of a line segment on the axes are $x_{1}, y_{1}, z_{1}$ then the length of the line segment is $\sqrt{{x_{1}}^{2} + {y_{1}}^{2} + {z_{1}}^{2}}$
The projections of a line segment on the axes are 1,2,2 and the length of the segment is $n$
Hence, $n = \sqrt{1 + 4 + 4} = 3$
It implies that $\log_{3} \sqrt{3} = 0.5$

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