VITEEE 2025 Paper

Let a,b,c, be the direction ratios of the required line. Then, equation of line passing through (1,2,−4) and having DR's ( a,b,c ) is
‌

x−1

a

=‌

y−2

b

=‌

z+4

c

Now, as line (i) is perpendicular to the lines ‌

x−8

3

=‌

y+19

−16

=‌

z−10

7

and

‌‌

x−15

3

=‌

y−29

8

=‌

z−5

−5

‌∴3a−16b+7c=0
‌3a+8b−5c=0
On solving (ii) and (iii), we get
‌

a

24

=‌

b

36

=‌

c

72

‌ i.e., ‌‌

a

2

=‌

b

3

=‌

c

6

So, the required equation is
‌

x−1

2

=‌

y−2

3

=‌

z+4

6