
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Miscellaneous
Misc 2 Important
Misc 3 Important
Misc 4 Important
Misc 5 Important
Question 1 Important Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Question 4 Deleted for CBSE Board 2024 Exams
Question 5 Important Deleted for CBSE Board 2024 Exams You are here
Question 6 Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 8 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 12 Deleted for CBSE Board 2024 Exams
Question 13 Important Deleted for CBSE Board 2024 Exams
Question 14 Important Deleted for CBSE Board 2024 Exams
Question 15 Deleted for CBSE Board 2024 Exams
Question 16 Important Deleted for CBSE Board 2024 Exams
Question 17 (MCQ) Important Deleted for CBSE Board 2024 Exams
Question 18 (MCQ) Important Deleted for CBSE Board 2024 Exams
Miscellaneous
Last updated at May 29, 2023 by Teachoo
Question 5 Find the equation of the plane passing through (a, b, c) and parallel to the plane 𝑟 ⃗ . (𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂) = 2.The equation of plane passing through (x1, y1, z1) and perpendicular to a line with direction ratios A, B, C is A(x − x1) + B (y − y1) + C(z − z1) = 0 The plane passes through (a, b, c) So, x1 = 𝑎, y1 = 𝑏, z1 = 𝑐 Since both planes are parallel to each other, their normal will be parallel ∴ Direction ratios of normal = Direction ratios of normal of 𝑟 ⃗.(𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂) = 2 Direction ratios of normal = 1, 1, 1 ∴ A = 1, B = 1, C = 1 Thus, Equation of plane in Cartesian form is A(x − x1) + B (y − y1) + C(z − z1) = 0 1(x − 𝑎) + 1(y − b) + 1(z − c) = 0 x − a + y − b + z − c = 0 x + y + z − (a + b + c) = 0 x + y + z = a + b + c ∴ Direction ratios of normal = Direction ratios of normal of 𝑟 ⃗.(𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂) = 2 Direction ratios of normal = 1, 1, 1 ∴ A = 1, B = 1, C = 1 Thus, Equation of plane in Cartesian form is A(x − x1) + B (y − y1) + C(z − z1) = 0 1(x − 𝑎) + 1(y − b) + 1(z − c) = 0 x − a + y − b + z − c = 0 x + y + z − (a + b + c) = 0 x + y + z = a + b + c