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ANALYTIC GEOMETRY II

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Learning Outcomes

  • define vector concept in the space.
  • interpret vector concept in space geometrically.
  • apply algebraic properties of vectors in exercises.
  • interpret cross product of two vectors in space geometrically.
  • interpret dot and cross product of two vectors in space geometrically.
  • translate equations of line in space.
  • express equation of the line whose a point and direction are given
  • describe equation of the line passing through two points.
  • identify conditions of two lines' being perpendicular or parallel.
  • express equation of the line that passes through a point and is perpendicular to two lines.
  • translate equations of plane in space.
  • express equation of the plane that passes through a point and is perpendicular to the given line.
  • describe equation of the plane which passes through three points.
  • determine equation of the plane that passes through a point and is parallel to two directions.
  • analyse many problems related to a line and plane in the space.
  • calculate distance from a point to a line
  • calculate distance between two lines
  • calculate distance from a point to a plane.
  • define surfaces.
  • formulate equation of surfaces on cartesian coordinates.
  • draw any surface chart.
  • express intersection curve of two surfaces.
  • explain a sphere.
  • express a cylinder.
  • define an ellipsoid.
  • express hyperboloid of one and two sheets.
  • express an elliptic paraboloid.
  • interpret intersection of the conics with plane geometrically.
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