

Get live Maths 1-on-1 Classs - Class 6 to 12
Miscellaneous
Misc 2
Misc 3
Misc 4 Important
Misc 5 Important
Misc 6 Important
Misc 7 Deleted for CBSE Board 2023 Exams
Misc 8 Important Deleted for CBSE Board 2023 Exams You are here
Misc 9 Important
Misc 10 Deleted for CBSE Board 2023 Exams
Misc 11 Important Deleted for CBSE Board 2023 Exams
Misc 12 Important Deleted for CBSE Board 2023 Exams
Misc 13 Important Deleted for CBSE Board 2023 Exams
Misc 14 Important Deleted for CBSE Board 2023 Exams
Misc 15 Important Deleted for CBSE Board 2023 Exams
Misc 16 Deleted for CBSE Board 2023 Exams
Misc 17 Important Deleted for CBSE Board 2023 Exams
Misc 18 Important Deleted for CBSE Board 2023 Exams
Misc 19 Deleted for CBSE Board 2023 Exams
Misc 20 Important
Misc 21 Important Deleted for CBSE Board 2023 Exams
Misc 22 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 23 (MCQ) Important Deleted for CBSE Board 2023 Exams
Miscellaneous
Last updated at March 16, 2023 by Teachoo
Misc 8 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