UPSC NDA Math Model Paper 3

It is given that the line is equally inclined to the co-ordinate axes.
Therefore, the direction cosines of the line are (

1

√3

,

1

√3

,

1

√3

)
It is given that the line passes through (-3, 2, -5)
Therefore, we have (x1,y1,z1)=(−3,2,−5) and (a,b,c)=(

1

√3

,

1

√3

,

1

√3

).
Thus, the equation of the line is given as follows:

x+3

1 √3

=

y−2

1 √3

=

z+5

1 √3

=k
∴

x+3

1

=

y−2

1

=

z+5

1