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UPSC NDA 2 2019 Mathematics Solved Paper

Question : 57 of 120

Marks: +1, -0

\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+2}{7}

has coordinates

Solution:

Concept:

A point on a line in symmetric form can be expressed using a parameter

k

, where each coordinate is expressed in terms of

k

Explanation:

Given the line:

\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+2}{7} = k

Then

x = k + 1

y = 2k + 3

, and

z = 7k - 2

Any point on the line has coordinates

(k+1, 2k+3, 7k-2)

Substitute

k=1

(1+1, 2(1)+3, 7(1)-2) = (2, 5, 5)

This matches option B.

Answer:

(2, 5, 5)

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