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Question 24 (B) A person standing at 𝑶(𝟎,𝟎,𝟎) is watching an aeroplane which is at the coordinate point 𝑨(𝟒,𝟎,𝟑). At the same time he saw a bird at the coordinate point 𝑩(𝟎,𝟎,𝟏). Find the angles which (𝐵𝐴) ⃗ makes with the x,y and z axes.Now, Angles which (𝑩𝑨) ⃗ makes with the x,y and z axes = Direction cosines of (𝑩𝑨) ⃗ Given A (4, 0, 3) & B (0, 0, 1) So, x1 = 4, y1 = 0, z1 = 3 & x2 = 0, y2 = 0, z2 = 1 Direction ratios = (x2 – x1), (y2 − y1), (z2 − z1) = 0 − 4, 0 − 0, 1 − 3 = −4, 0, −2 And, Direction cosines = (−4)/√((−4)2+02+ (−2)2) , ( 0)/√((−4)2+02+ (−2)2) , (−2)/√((−4)2+02+ (−2)2) = (−4)/√(16 + 0 + 4) , 0 , (−2)/√(16 + 0 + 4) = (−4)/√20 , 0 , (−2)/√20 = (−4)/√(4 × 5) , 0 , (−2)/√(4 × 5) = (−4)/(2√5) , 0 , (−2)/(2√5) = (−𝟐)/√𝟓 , 𝟎 , (−𝟏)/√𝟓 Now, we know that Direction cosines of a line making, 𝛼 with x – axis, 𝛽 with y – axis, and 𝛾 with z – axis are l,m,n l = cos 𝜶, m = cos 𝜷, n = cos 𝜸 So, cos 𝛼 = (−2)/√5 𝜶 = 〖𝒄𝒐𝒔〗^(−𝟏)⁡((−𝟐)/√𝟓) cos 𝛽 = 0 𝜷 = 𝜋/𝟐 cos 𝛾 = (−1)/√5 𝜸 = 〖𝒄𝒐𝒔〗^(−𝟏)⁡((−𝟏)/√𝟓) Thus, (𝐵𝐴) ⃗ makes angles 〖𝒄𝒐𝒔〗^(−𝟏)⁡((−𝟐)/√𝟓) , 𝝅/𝟐 , 〖𝒄𝒐𝒔〗^(−𝟏)⁡((−𝟏)/√𝟓) with the 𝐱,𝐲 and z axes respectively

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.