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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

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°