Plane

Question 1 (a)
Deleted for CBSE Board 2024 Exams

Question 1 (b) Deleted for CBSE Board 2024 Exams

Question 1 (c) Important Deleted for CBSE Board 2024 Exams

Question 1 (d) Important Deleted for CBSE Board 2024 Exams

Question 2 Deleted for CBSE Board 2024 Exams

Question 3 (a) Deleted for CBSE Board 2024 Exams

Question 3 (b) Deleted for CBSE Board 2024 Exams

Question 3 (c) Important Deleted for CBSE Board 2024 Exams

Question 4 (a) Important Deleted for CBSE Board 2024 Exams

Question 4 (b) Deleted for CBSE Board 2024 Exams

Question 4 (c) Deleted for CBSE Board 2024 Exams

Question 4 (d) Important Deleted for CBSE Board 2024 Exams

Question 5 (a) Important Deleted for CBSE Board 2024 Exams

Question 5 (b) Deleted for CBSE Board 2024 Exams

Question 6 (a) Important Deleted for CBSE Board 2024 Exams

Question 6 (b) Deleted for CBSE Board 2024 Exams

Question 7 Deleted for CBSE Board 2024 Exams

Question 8 Deleted for CBSE Board 2024 Exams

Question 9 Deleted for CBSE Board 2024 Exams

Question 10 Important Deleted for CBSE Board 2024 Exams You are here

Question 11 Important Deleted for CBSE Board 2024 Exams

Question 12 Important Deleted for CBSE Board 2024 Exams

Question 13 (a) Important Deleted for CBSE Board 2024 Exams

Question 13 (b) Important Deleted for CBSE Board 2024 Exams

Question 13 (c) Deleted for CBSE Board 2024 Exams

Question 13 (d) Deleted for CBSE Board 2024 Exams

Question 13 (e) Deleted for CBSE Board 2024 Exams

Question 14 (a) Important Deleted for CBSE Board 2024 Exams

Question 14 (b) Deleted for CBSE Board 2024 Exams

Question 14 (c) Deleted for CBSE Board 2024 Exams

Question 14 (d) Important Deleted for CBSE Board 2024 Exams

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

Last updated at April 16, 2024 by Teachoo

Question 10 Find the vector equation of plane passing through the intersection of the planes 𝑟 ⃗ . (2𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂) = 7, 𝑟 ⃗ .(2𝑖 ̂ + 5𝑗 ̂ + 3𝑘 ̂) = 9 and through the point (2, 1, 3).The vector equation of a plane passing through the intersection of planes 𝑟 ⃗. (𝑛1) ⃗ = d1 and 𝑟 ⃗. (𝑛2) ⃗ = d2 and also through the point (x1, y1, z1) is 𝒓 ⃗.((𝒏𝟏) ⃗ + 𝜆(𝒏𝟐) ⃗) = d1 + 𝜆d2 Given, the plane passes through The vector equation of a plane passing through the intersection of planes 𝑟 ⃗. (𝑛1) ⃗ = d1 and 𝑟 ⃗. (𝑛2) ⃗ = d2 and also through the point (x1, y1, z1) is 𝒓 ⃗.((𝒏𝟏) ⃗ + 𝜆(𝒏𝟐) ⃗) = d1 + 𝜆d2 Given, the plane passes through 𝒓 ⃗. (2𝒊 ̂ + 2𝒋 ̂ − 3𝒌 ̂) = 7 Comparing with 𝑟 ⃗.(𝑛1) ⃗ = 𝑑1, (𝑛1) ⃗ = 2𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂ & d1 = 7 𝒓 ⃗. (2𝒊 ̂ + 5𝒋 ̂ + 3𝒌 ̂) = 9 Comparing with 𝑟 ⃗.(𝑛2) ⃗ = 𝑑2, (𝑛2) ⃗ = 2𝑖 ̂ + 5𝑗 ̂ + 3𝑘 ̂ & d2 = 9 So, equation of the plane is 𝑟 ⃗.["(2" 𝑖 ̂+"2" 𝑗 ̂" " −"3" 𝑘 ̂")" +"𝜆(2" 𝑖 ̂" " + 5𝑗 ̂" " + "3" 𝑘 ̂")" ] = 7 + 𝜆.9 𝑟 ⃗. ["2" 𝑖 ̂" " +" 2" 𝑗 ̂" " − "3" 𝑘 ̂ + 2"𝜆" 𝑖 ̂ + 5"𝜆" 𝑗 ̂ + 3"𝜆" 𝑘 ̂ ] = 7 + 9"𝜆" 𝒓 ⃗. ["(2" +"2𝜆" )𝒊 ̂" " +"(2" +"5𝜆" )𝒋 ̂ +"(−" 𝟑+"3𝜆" )𝒌 ̂ ] = 9"𝜆" + 7 Now, to find 𝜆 , put 𝒓 ⃗ = x𝒊 ̂ + y𝒋 ̂ + z𝒌 ̂ (x𝑖 ̂ + y𝑗 ̂ + z𝑘 ̂).["(2 " + "2𝜆" )𝑖 ̂" " + "(2" +"5𝜆" )𝑗 ̂ +"(−" 3" " +" 3𝜆" )𝑘 ̂ ] = 9𝜆 + 7 x"(2 "+" 2𝜆")" "+ "y (2 "+" 5𝜆")𝑗 ̂ + 𝑧"("−3+"3𝜆")𝑘 ̂ = 9𝜆 + 7 The plane passes through (2, 1, 3) Putting (2, 1, 3) in (2), 2(2 + 2𝜆) + 1(2 + 5𝜆) + 3(−3 + 3𝜆) = 9𝜆 + 7 4 + 4𝜆 + 2 + 5𝜆 + (−9) + 9𝜆 = 9𝜆 + 7 18𝜆 − 9𝜆 = 7 + 3 9𝜆 = 10 ∴ 𝜆 = 𝟏𝟎/𝟗 Putting value of 𝜆 in (1), 𝑟 ⃗. [(2+ 2. 10/9) 𝑖 ̂ + (2+ 5. 10/9) 𝑗 ̂ +("−" 3+ 3. 10/9) 𝑘 ̂ ] = 9.10/9 + 7 𝑟 ⃗. [(2 + 20/9) 𝑖 ̂ +(2 + 50/9) 𝑗 ̂ +("−" 3 + 30/9) 𝑘 ̂ ] = 10 + 7 𝑟 ⃗. [38/9 𝑖 ̂+ 68/9 𝑗 ̂ + 3/9 𝑘 ̂ ] = 17 1/9 𝑟 ⃗. (38𝑖 ̂ + 68𝑗 ̂ + 3𝑘 ̂ ) = 17 𝑟 ⃗.(38𝑖 ̂+68𝑗 ̂+3𝑘 ̂ ) = 17 × 9 𝒓 ⃗.(𝟑𝟖𝒊 ̂+𝟔𝟖𝒋 ̂+𝟑𝒌 ̂ ) = 153