Find a and b So That Surfaces Are Orthogonal at a Point | VTU Vector Calculus скачать в хорошем качестве

Find a and b So That Surfaces Are Orthogonal at a Point | VTU Vector Calculus

🎓 Find a and b such that Two Surfaces Are Orthogonal | VTU Engineering Mathematics | BMATS201 / BMATM201 / BMATE201 / BMATC201 In this video, we solve an advanced conceptual problem from Vector Calculus that asks us to find the values of parameters a and b such that two given surfaces are orthogonal at a specific point. This involves using gradient vectors and the dot product condition for orthogonality. 🧩 Problem Statement: Find the value of a and b, such that the surfaces ax²+byz=(a+2)x and 4x²y+z³=4 are orthogonal at the point (1,-1,2) 📘 Subject Codes & Modules: ✅ BMATS201 – Module 2 (CSE / ISE / AI-ML) ✅ BMATM201 – Module 2 (Mechanical – NEP Scheme) ✅ BMATE201 – Module 1 (ECE / EEE / EIE) ✅ BMATC201 – Module 2 (Civil / Mech / Auto) 📌 Concepts Covered in This Video: ✅ Using gradients as normals to surfaces ✅ Orthogonality condition via dot product = 0 ✅ Applying multivariable calculus to find unknowns ✅ Solving step-by-step using substitution and evaluation at a point 🎯 This is a most expected question for VTU CBCS/NEP Engineering Maths-II exams. 🎓 If you're a university student — whether you're pursuing B.Tech, B.Sc, or any related degree — and this chapter or topic is part of your syllabus, this video will definitely help you understand it better. Don’t miss it! [ 🕕 Watch Next ] 1. Unit Normal Vector to a Surface →    • Find Unit Normal Vector to a Surface at a ...   2. Normal Vector | Surface xy³z² = 4 →    • BMATS201 Module 2 ( Vector Calculus ) updated   3. Normal Vector | Surface Solved →    • Unit Normal Vector from Gradient | Surface...   4. Directional Derivative (1/7) →    • Vector Calculus : Directional Derivative (...   5. Directional Derivative (2/7) →    • Vector Calculus : Directional Derivative (...   6. Directional Derivative (3/7) →    • Vector Calculus : Directional Derivative (...   7. Directional Derivative (4/7) →    • Vector Calculus : Directional Derivative (...   8. Directional Derivative (5/7) →    • Vector Calculus : Directional Derivative (...   9. Directional Derivative (6/7) →    • Vector Calculus : Directional Derivative (...   10. Directional Derivative (7/7) →    • Vector Calculus : Directional Derivative (...   11. Angle Between Surfaces (1/2) →    • Vector Calculus : Angle between two surfac...   12. Angle Between Surfaces (2/2) →    • Vector Calculus : Angle between two surfac...   13. Angle Between Normals →    • Vector Calculus : Angle between normal to ...   14. Surfaces Orthogonal at a Point →    • Find a and b So That Surfaces Are Orthogon...   15. Div & Curl of ∇(xy³z²) @ (1,–1,1) →    • Find Divergence and Curl of ∇(xy³z²) at (1...   16. Div & Curl of ∇(x³+y³+z³) →    • Divergence and Curl of ∇(x³ + y³ + z³) | V...   17. Prove Solenoidal & Irrotational →    • Prove Vector Field Is Solenoidal and Irrot...   18. Find a, b, c | Irrotational Fields →    • Find a, b, c for Irrotational Vector Field...   19. Find a & b | Solenoidal & Irrotational →    • Find a & b So That Vector Field Is Solenoi...   20. Prove Irrotational & Find φ →    • Prove Vector Field Is Irrotational and Fin...   [ 🕕 Playlists ] BMATS201: M1 –    • BMATS201 Module 1 ( Integral Calculus - Mu...   M2 –    • Engineering Maths: Vector Calculus (Gradie...   M3 –    • Vector Space & Linear Transformation   M4 –    • BMATS201 Module 4 ( Numerical Methods 1)   M5 –    • Numerical Methods 2 ( Numerical Solution o...   BMATE201: M1 –    • Engineering Maths: Vector Calculus (Gradie...   M2 –    • Vector Space & Linear Transformation   M3 –    • Bmate201 module 4 ( Numerical Methods 1 )   M4 –    • Bmate201 module 4 ( Numerical Methods 1 )   M5 –    • Numerical Methods 2 ( Numerical Solution o...   BMATC201: M1 –    • BMATC201 Module 1 ( Integral Calculus - Mu...   M2 –    • Engineering Maths: Vector Calculus (Gradie...   M3 –    • Partial Differential Equations   M4 –    • Bmatc201 module 4 ( Numerical Methods 1 )   M5 –    • Numerical Methods 2 ( Numerical Solution o...   BMATM201: M1 –    • BMATM201 Module 1 ( Integral Calculus - Mu...   M2 –    • Engineering Maths: Vector Calculus (Gradie...   M3 –    • Partial Differential Equations   M4 –    • Bmatm201 module 4 ( Numerical Methods 1 )   M5 –    • Numerical Methods 2 ( Numerical Solution o...   #EngineeringMathematics #VectorCalculus #VTUMaths #BMATS201 #BMATM201 #BMATE201 #BMATC201 #VTUModule2 #OrthogonalSurfaces #GradientVector #DotProduct #FindAandB #MultivariableCalculus #VTUNEP #VTCBCS #EngineeringMaths2 #BTechMaths #MathsForEngineers #VTUImportantQuestions