The d. r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x+y=3 are

[b] Equation of plane through (1, 0, 0) is a(x−1)+by+cz=0                      (i) (i) Passes through (0, 1, 0). −a+b=0 ⇒b=a; Also, cos45∘=a+a2(2a2+c2)−−−−−−−−−√⇒2a=2a2+c2−−−−−−−√ ⇒2a2=c2⇒c=2a−−√. So. d. r of normal area a,a2a−−√ i.e., 1,1,2√.