Example 21
Last updated at March 11, 2017 by Teachoo
Transcript
Example 21 (Introduction) Show that the points A(−2 𝑖 + 3 𝑗 + 5 𝑘), B( 𝑖 + 2 𝑗 + 3 𝑘) and C(7 𝑖 − 𝑘) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three vectors collinear i.e. 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶 Example 21 Show that the points A(−2 𝑖 + 3 𝑗 + 5 𝑘), B( 𝑖 + 2 𝑗 + 3 𝑘) and C(7 𝑖 − 𝑘) are collinear. 3 points A, B, C are collinear if 𝑨𝑩 + 𝑩𝑪 = 𝑨𝑪 A (−2 𝑖 + 3 𝑗 + 5 𝑘) B (1 𝑖 + 2 𝑗 + 3 𝑘) C (7 𝑖 + 0 𝑗 − 1 𝑘) 𝐴𝐵 = (1 – (-2)) 𝑖 + (2 − 3) 𝑗 + (3 − 5) 𝑘 = 3 𝑖 – 1 𝑗 – 2 𝑘 𝐵𝐶 = (7 − 1) 𝑖 + (0 − 2) 𝑗 + (-1−3) 𝑘 = 6 𝑖 – 2 𝑗 – 4 𝑘 𝐴𝐶 = (7 − (-2)) 𝑖 + (0 − 3) 𝑗 + (-1 − 5) 𝑘 = 9 𝑖 – 3 𝑗 – 6 𝑘 Magnitude of 𝐴𝐵 = 32+ −12+ −22 𝐴𝐵 = 9+1+4 = 𝟏𝟒 Magnitude of 𝐵𝐶 = 62+ −22+ −42 𝐵𝐶 = 36+4+16 = 56 = 4×14 = 2 𝟏𝟒 Magnitude of 𝐴𝐶 = 92+ −32+ −62 𝐴𝐶 = 81+9+36 = 126 = 9×14 = 3 𝟏𝟒 Thus, 𝐴𝐵 + 𝐵𝐶 = 14 + 2 14 = 3 14 = 𝐴𝐶 Thus, A, B and C are collinear.
Examples
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Example 21 Important You are here
Example 22
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Example 24 Important
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Example 26
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Example 26 (Supplementary NCERT)
Example 27 (Supplementary NCERT)
Example 28 (Supplementary NCERT)
Example 29 (Supplementary NCERT)
Example 30 (Supplementary NCERT)
Example 31 (Supplementary NCERT)
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.