Answers

2014-03-04T13:40:34+05:30
Z=x²+y²-1 => x²+y²-z=1    ........(i)
x²+y²+z²=4    ............(ii)
Δ(x²+y²-z) = [2x, 2y, -1z]
Δ(x²+y²+z²) = [2x, 2y, 2z]
The tangent vector at the point are (1, 0, -1)
Therefore, A = (2, 0, 2)
               B = (2, 0, -2)
Therefore, the product of this two vectors are,
A x B = 2 x 2 + 0 x 0 + 2 x -2
         = 4 + 0 - 4
         = 0
Again, A x B = ΙAΙ ΙBΙ cosθ
The magnitude of the two vectors,
ΙAΙ = √2² + 0² + 2² = √8
ΙBΙ = √2² + 0² + -2² = √8
Now, substituting the values,
A x B = ΙAΙ ΙBΙ cosθ
      0  = √8 x √8 x cosθ
      0  = (√8)² x cosθ
      0  = 8 x cosθ
  cosθ = 0
  cosθ = cos90°
       θ = 90°
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