Ex 11.1, 5 - Find direction cosines of sides of triangle - Ex 11.1

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  1. Chapter 11 Class 12 Three Dimensional Geometry
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Ex 11.1, 5 - Chapter 11 Class 12 Three Dimensional Geometry - NCERT Solution Find the direction cosines of the sides of the triangle whose vertices are (3, 5, -4), ( -1, 1, 2) and (-5, -5, -2). Direction ratios of a line passing through two points P(x1, y1, z1,), & Q (x2, y2, z2) = (x2 โ€“ x1), (y2 โˆ’ y1), (z2 โˆ’ z1) Direction cosines = (๐‘ฅ2 โˆ’ ๐‘ฅ1)/๐‘ƒ๐‘„ , (๐‘ฆ2 โˆ’ ๐‘ฆ1)/๐‘ƒ๐‘„ , (๐‘ง2 โˆ’ ๐‘ง1)/๐‘ƒ๐‘„ where, PQ = โˆš((๐‘ฅ2โˆ’๐‘ฅ1)^2+(๐‘ฆ2โˆ’๐‘ฆ1)^2+(๐‘ง2โˆ’๐‘ง1)^2 ) AB A (3, 5, โˆ’4) B( โˆ’1, 1, 2) Direction ratios = โˆ’1 โˆ’ 3, 1 โˆ’ 5, 2 โˆ’(โˆ’4) = โˆ’ 4, โˆ’ 4, 6 AB = โˆš68 = โˆš(4 ร— 17 ) = 2โˆš17 Direction cosines = ( โˆ’4)/(2โˆš17) , ( โˆ’4)/(2โˆš17) , 6/(2โˆš17) = (โˆ’๐Ÿ)/โˆš๐Ÿ๐Ÿ• , (โˆ’๐Ÿ)/โˆš๐Ÿ๐Ÿ• , ๐Ÿ‘/โˆš๐Ÿ๐Ÿ• BC B ( โˆ’1, 1, 2) C ( โˆ’5, โˆ’5, โˆ’2) Direction ratios = โˆ’5 โˆ’(โˆ’1), โˆ’5โˆ’1 , โˆ’2โˆ’2 = โ€“4, โˆ’6, โˆ’4 BC = โˆš68 = โˆš(4 ร— 17 ) = 2โˆš17 Direction cosines = ( โˆ’4)/(2โˆš17) , (โˆ’6)/(2โˆš17) , ( โˆ’4)/(2โˆš17) = (โˆ’๐Ÿ)/โˆš๐Ÿ๐Ÿ• , (โˆ’๐Ÿ‘)/โˆš๐Ÿ๐Ÿ• , (โˆ’๐Ÿ)/โˆš๐Ÿ๐Ÿ• CA C ( โˆ’5, โˆ’5, โˆ’2) A (3, 5, โˆ’ 4) Direction ratios =3โˆ’(-5), 5โˆ’(-5), โˆ’4โˆ’(-2) = 8, 10 , โ€“2 CA = โˆš168 = โˆš(4 ร— 42 )= 2โˆš42 Direction cosines = ( 8)/(2โˆš42) , ( 10)/(2โˆš42) , (โˆ’2)/(2โˆš42) = ( ๐Ÿ’)/โˆš๐Ÿ’๐Ÿ , ( ๐Ÿ“)/โˆš๐Ÿ’๐Ÿ , (โˆ’๐Ÿ)/โˆš๐Ÿ’๐Ÿ

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.