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UPSC NDA I 2015 Mathematics Paper

Question Numbers: 53-54

The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively.

Question : 53 of 120

Marks: +1, -0

What is the length of the line segment?

Solution:

Concept:

The length of a line segment represented by a vector

\vec{a}=x\vec{i}+y\vec{j}+z\vec{k}

is its magnitude:

|\vec{a}|=\sqrt{x^2+y^2+z^2}

Explanation:

For the given line segment, the vector components are

x=12

y=4

, and

z=3

Thus,

\vec{a}=12\vec{i}+4\vec{j}+3\vec{k}

The length is

|\vec{a}|=\sqrt{12^2+4^2+3^2}

Calculate:

12^2=144

4^2=16

3^2=9

Sum:

144+16+9=169

Square root:

\sqrt{169}=13

Hence, the length is 13 units.

Answer:

13 units (Option D).

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