Given, l+m−n=0. . . (i) and I2+m2−n2=0‌‌... (ii) On squaring Eq. (i), we get (l+m)2=n2 ⇒‌‌l2+m2+2lm=n2 . . . (iii) From Eqs. (ii) and (iii), I2+m2−n2=0 I2+m2+2lm=n2 ‌
−−‌‌−‌‌−
−n2−2lm=−n2
⇒‌‌2lm=0⇒Im=0 ⇒‌‌I=0‌ or ‌m=0 ‌ Case I When I = 0 ‌ ⇒‌‌0+m−n=0 ⇒‌‌m=n ‌ and ‌I2+m2+n2=1 ⇒‌‌m2+m2=1‌‌[∵n=m and l=0] ⇒‌‌m2=‌
1
2
‌‌‌m=±‌
1
√2
=n ∴‌‌(I,m,n)=(0,‌
1
√2
,‌
1
√2
)‌ or ‌(0,‌
−1
√2
,‌
−1
√2
) Case II When m=0 then, l+m−n=0 ⇒‌‌I=n and l2+m2+n2=1 [∵n=I and m=0] ⇒‌‌I2+0+I2=1 I=±‌