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GATE Question
The equation of the plane that is tangent to the surface xyz = 8 at point (1,2,4) is
  • a)
    x + 2y + 4z = 12
  • b)
    4x + 2y + z = 12
  • c)
    x + 4y + 2z = 12
  • d)
    x + y + z = 7
Correct answer is option 'B'. Can you explain this answer?

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Answers

Kaushalaya Devi
Aug 24, 2020
Suppose T(x,y,z) be any point on tangent plane  is normal to surface  at point P(1,2,4). Therefore,  is perpendicular to vector  lying in the tangent plane of the given surface.

By placing values x≈1, y=2, z=4 we get
4+4+4= 12
12=12

Suppose T(x,y,z) be any point on tangent planeis normal to surfaceat point P(1,2,4). Therefore,is perpendicular to vectorlying in the tangent plane of the given surface.

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Suppose T(x,y,z) be any point on tangent planeis normal to surfaceat point P(1,2,4). Therefore,is perpendicular to vectorlying in the tangent plane of the given surface.
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