UPSC NDA Math Model Paper 10

Given: Equation of line

x−6

3

=

y−2

−4

=

z+7

5

and point (1, - 2, 3)
Let A = (1, - 2, 3)
Here we have to find the equation of line parallel to

x−6

3

=

y−2

−4

=

z+7

5

and passing through point A.
As we know that, if two lines are parallel then their direction ratios are same
So, the direction ratios of the required line is same as that of

x−6

3

=

y−2

−4

=

z+7

5

which are: 3, - 4, 5
As we know that equation of line with direction ratio's a, b, c and passing through point A(x1,y1,z1) is given by:

x−x1

a

=

y−y1

b

=

z−z1

c

Hence, the equation of required line is:

x−1

3

=

y+2

−4

=

z−3

5