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Supplementary Example 5 - Show that four points with position - Supplementary examples and questions from CBSE

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Supplementary Example 5 Show that the four points with position vectors 6 𝑖īˇ¯ − 7 𝑗īˇ¯, 16 𝑖īˇ¯ − 19 𝑗īˇ¯ − 4 𝑘īˇ¯, 3 𝑗īˇ¯ − 6 𝑘īˇ¯ and 2 𝑖īˇ¯ + 5 𝑗īˇ¯ + 10 𝑘īˇ¯ are not co-planar Let points be A = 6 𝑖īˇ¯ – 7 𝑗īˇ¯ B = 16 𝑖īˇ¯ – 19 𝑗īˇ¯ – 4 𝑘īˇ¯ C = 3 𝑗īˇ¯ – 6 𝑘īˇ¯ D = 2 𝑖īˇ¯ + 5 𝑗īˇ¯ +10 𝑘īˇ¯ Four points A, B, C, D are coplanar if the three vectors 𝐴đĩīˇ¯ , 𝐴đļīˇ¯ and 𝐴𝐷īˇ¯ are coplanar. i.e. 𝑨𝑩īˇ¯, 𝑨đ‘Ēīˇ¯, 𝑨đ‘Ģīˇ¯īˇ¯ = 0 = 10 100+72īˇ¯+12 −60−24īˇ¯âˆ’4 −72+40īˇ¯ = 10 172īˇ¯+12 −84īˇ¯âˆ’4 −32īˇ¯ = 1720 – 1008 + 128 = 840 ∴ 𝑨𝑩īˇ¯, 𝑨đ‘Ēīˇ¯, 𝑨đ‘Ģīˇ¯īˇ¯ ≠ 0 Therefore, points A, B, C and D are not coplanar.

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