Project ForgeEngineering Mathematics
Calculus
GATE 2012
Easy
For the spherical surface x²+y²+z²=1, the unit outward normal vector at the point (1/√2, 1/√2, 0) is given by
- (1/√2)î + (1/√2)ĵ
- B(1/√2)î − (1/√2)ĵ
- Ck̂
- D(1/√3)î + (1/√3)ĵ + (1/√3)k̂
Explanation
The outward unit normal to a level surface F(x,y,z)=x²+y²+z²=1 is ∇F/|∇F| = (2x,2y,2z)/|(2x,2y,2z)| = (x,y,z)/√(x²+y²+z²). Since the given point already lies on the unit sphere, x²+y²+z²=1, so the normal is simply (x,y,z) itself = (1/√2, 1/√2, 0).
Source: GATE ME 2012 (Booklet Code A) (2012)
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