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UPSC NDA I 2016 Mathematics Solved Paper

For the next three (3) items that follow :

A plane P passes through the line of intersection of the planes

2x-y+3z=2,x+y-z=1

and the point

(1,0,1)

[NDA I 2016]

Question : 65 of 120

Marks: +1, -0

Solution:

To find intersection point first put

z=0

2x-y=2

\;\;x+y=1

–––––––––––

3x=3

x=1

x+y=1

y=1-x

x=1,y=0

(x,y,z)\equiv(1,0,0)

Putting

x=0

y-z=1

-y+3z=2

–––––––––––––

2z=3

z=\frac{3}{2}

y=1+z=1+\;\;\frac{3}{2}=\;\;\frac{5}{2}

(x,y,z)\equiv\left(0,\;\;\frac{5}{2},\;\;\frac{3}{2}\right)

Point of intersection

(x_{1},y_{1},z_{1})\equiv(1,0,0)

(x_{2},y_{2},z_{2})\equiv(0,\;\;\frac{5}{2},\;\;\frac{3}{2}

)

Hence direction ratios of the line of intersection of given plane

\langle 2,-5,-3 \rangle

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