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UPSC NDA I 2015 Mathematics Paper

Question Numbers: 57-58

Directions: For the next two (2) items that follow:

A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C respectively.

Question : 57 of 120

Marks: +1, -0

What are the intercepts made by the plane ABC on the axes?

Solution:

Concept:

The centroid of a triangle formed by the intercept points on the axes is given by the average of their coordinates.

Explanation:

Let the plane ABC intersect the axes at points

A(a,0,0)

B(0,b,0)

, and

C(0,0,c)

The centroid of triangle

ABC

\left( \frac{a+0+0}{3}, \frac{0+b+0}{3}, \frac{0+0+c}{3} \right)

Given centroid is

(1,2,3)

Equate coordinates:

\frac{a}{3}=1 \Rightarrow a=3

\frac{b}{3}=2 \Rightarrow b=6

\frac{c}{3}=3 \Rightarrow c=9

Thus intercepts on x, y, z axes are

3

6

, and

9

respectively.

Answer:

Option A: 3, 6, 9.

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