6.8.4 Equation of a plane passing through three given non-collinear points
Chapter 6: Chapter 6 · MATHEMATICS-VOLUME 1 · EN medium
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(a) Parametric form of vector equation Theorem . If three non-collinear points with position vectors , , a b c are given, then the vector equation of the plane passing through the given points in parametric form is s b t c , where , ≠ ≠ and , s t ∈ . Proof Consider a plane passing through three non-collinear points , , A B C with position vectors , , a b c respectively. Then atleast two of them are non-zero vectors. Let us take b ≠ and c ≠ . Let r be the position vector of an arbitrary point P on the plane. Take a point D on AB (produced) such that AD is parallel to AB and DP is parallel to AC . Therefore,
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 268
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(a) Parametric form of vector equation Theorem . If three non-collinear points with position vectors , , a b c are given, then the vector equation of the plane passing through the given points in parametric form is s b t c , where , ≠ ≠ and , s t ∈ . Proof Consider a plane passing through three non-collinear points , , A B C with position vectors , , a b c respectively. Then atleast two of them are non-zero vectors.
Let us take b ≠ and c ≠ . Let r be the position vector of an arbitrary point P on the plane. Take a point D on AB (produced) such that AD is parallel to AB and DP is parallel to AC . Therefore,
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