Given, a−b+c=0 ⇒‌‌b=a+c....(i) and ‌‌a2−b2+2c2=0 ⇒‌‌a2−(a+c)2+2c2=0[using Eq. (i)] ⇒a2−a2−c2−2ac+2c2=0 ⇒c2−2ac=0 ⇒c(c−2a)=0 ⇒c=0‌ or ‌c=2a When c=0, then b=a and when c=2a, then b=3a ‌a=a,b=a,c=0 ‌‌
d
a
=‌
b
a
=‌
c
0
.....(ii) ‌a=a,b=3a,c=2a ‌‌
a
a
=‌
b
3a
=‌
c
2a
...(iii) ∴ Direction ratios of Eq. (ii) are (1,1,0) and direction ratios of (iii) are (1,3,2).