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

Transcript

Supplementary Example 5 Show that the four points with position vectors 6 đ‘–īˇ¯ − 7 đ‘—īˇ¯, 16 đ‘–īˇ¯ − 19 đ‘—īˇ¯ − 4 đ‘˜īˇ¯, 3 đ‘—īˇ¯ − 6 đ‘˜īˇ¯ and 2 đ‘–īˇ¯ + 5 đ‘—īˇ¯ + 10 đ‘˜īˇ¯ are not co-planar Let points be A = 6 đ‘–īˇ¯ – 7 đ‘—īˇ¯ B = 16 đ‘–īˇ¯ – 19 đ‘—īˇ¯ – 4 đ‘˜īˇ¯ C = 3 đ‘—īˇ¯ – 6 đ‘˜īˇ¯ D = 2 đ‘–īˇ¯ + 5 đ‘—īˇ¯ +10 đ‘˜īˇ¯ Four points A, B, C, D are coplanar if the three vectors 𝐴đĩ , 𝐴đļ and đ´đˇīˇ¯ are coplanar. i.e. đ‘¨đ‘Šīˇ¯, 𝑨đ‘Ē, 𝑨đ‘Ģ = 0 = 10 100+72+12 −60−24īˇ¯âˆ’4 −72+40 = 10 172+12 −84īˇ¯âˆ’4 −32 = 1720 – 1008 + 128 = 840 ∴ đ‘¨đ‘Šīˇ¯, 𝑨đ‘Ē, 𝑨đ‘Ģ ≠ 0 Therefore, points A, B, C and D are not coplanar.

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