Question
Prove that the necessary and sufficient condition for any four points in three-dimensional space to be coplanar is that there exists a liner relation connecting their position vectors such that the algebraic sum of the coefficients (not all zero) in it is zero.
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Question 1
Suppose that are three non-coplanar vectors in . Let the components of a vector along be 4, 3 and 5, respectively. If the components of this vector along are x, y and z, respectively, then the value of is Question 2
Suppose that are three non-coplanar vectors in . Let the components of a vector along be 4, 3 and 5, respectively. If the components of this vector along are x, y and z, respectively, then the value of is Stuck on the question or explanation?
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Question Text | Prove that the necessary and sufficient condition for any four points in three-dimensional space to be coplanar is that there exists a liner relation connecting their position vectors such that the algebraic sum of the coefficients (not all zero) in it is zero. |