# Supplementary Example 5

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Supplementary Example 5 Show that the four points with position vectors 6 đīˇ¯ â 7 đīˇ¯, 16 đīˇ¯ â 19 đīˇ¯ â 4 đīˇ¯, 3 đīˇ¯ â 6 đīˇ¯ and 2 đīˇ¯ + 5 đīˇ¯ + 10 đīˇ¯ are not co-planar Let points be A = 6 đīˇ¯ â 7 đīˇ¯ B = 16 đīˇ¯ â 19 đīˇ¯ â 4 đīˇ¯ C = 3 đīˇ¯ â 6 đīˇ¯ D = 2 đīˇ¯ + 5 đīˇ¯ +10 đīˇ¯ Four points A, B, C, D are coplanar if the three vectors đ´đĩīˇ¯ , đ´đļīˇ¯ and đ´đˇīˇ¯ are coplanar. i.e. đ¨đŠīˇ¯, đ¨đĒīˇ¯, đ¨đĢīˇ¯īˇ¯ = 0 = 10 100+72īˇ¯+12 â60â24īˇ¯â4 â72+40īˇ¯ = 10 172īˇ¯+12 â84īˇ¯â4 â32īˇ¯ = 1720 â 1008 + 128 = 840 â´ đ¨đŠīˇ¯, đ¨đĒīˇ¯, đ¨đĢīˇ¯īˇ¯ â 0 Therefore, points A, B, C and D are not coplanar.

Supplementary examples and questions from CBSE

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Supplementary Example 5 You are here

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Supplementary Exercise Q5

Supplementary Exercise Q6

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.