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Linear algebra and geometry

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In the euclidean space let us consider the points

Which of the following statements is true?

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Let the versors of the coordinate axes of . For every , let us consider the vectors

Which of the following statements is true?

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Consider the points and and the lines 

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Given the plane and the straight line , find the correct statement.

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Given the straight lines 

find the right statement.

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In the euclidean 3-dimensional space with a fixed cartesian system, let us consider the circle defined by equations

Which of the following statements is true?

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Consider the circle

Which of the following spheres contains , that is ?

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Consider the circle

Which of the following spheres contains , that is ?

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In the 3-dimensional euclidian space with fixed orthogonal cartesian coordinate system let us consider the two circumferences 

Find the correct statement.

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In the euclidean 3-dimensional space with a fixed cartesian system, let us consider the circle defined by equations

Which of the following statements is true?

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