Calculating the Angle Between Two Surfaces: x² + y² + z² = 9 and x² + y² + z = 3 at Point (2, -1, 2)

Calculating the Angle Between Two Surfaces: x² + y² + z² = 9 and x² + y² + z = 3 at Point (2, -1, 2) | Bhagvati classes

Is video me mistek ho gaya tha solve kar di hu aap ise download karke right ans dekh lijiyega
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✅ About this video
Welcome to our YouTube video on calculating the angle between two surfaces! In this tutorial, we'll explore the mathematical process of determining the angle between two specific surfaces: x² + y² + z² = 9 and x² + y² + z = 3.

At the point (2, -1, 2), we will apply the necessary equations and techniques to find the angle between these surfaces. By utilizing concepts from vector calculus and differential geometry, we'll guide you through step-by-step calculations to arrive at the desired angle.

Understanding angles between surfaces is crucial in various fields such as physics, engineering, and computer graphics. So, whether you're a student seeking clarity or a curious learner eager to expand your mathematical knowledge, this video is perfect for you.

Join us as we dive into the calculations and provide clear explanations along the way. Don't worry if you're new to the topic – we'll make sure to cover all the necessary background information to help you follow along easily.

Stay tuned for this enlightening video, where we unravel the mystery behind the angle between two surfaces and empower you with a valuable mathematical skill. Don't forget to like, subscribe, and hit the notification bell to stay updated with our future content. Let's embark on this mathematical journey together!

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[BhagvatiClasses]

Is video me mistek ho gaya tha solve kar di hu aap ise download karke right ans dekh lijiyega
Sorry

[mdkyamuddinkhan]

Mam aap dz/dz=1 to aap waha par 2K kar di hai waha only k hoga or ans 8/3√21 😢hoga❤😉

[Forever_For_Sanatan]

Ok, sabse pehle humein surfaces ke gradient vectors nikalne hain. Gradient vector ka direction normal hota hai surface ke tangent plane ka.

Surface 1: \(x^2 + y^2 + z^2 = 9\)
Gradient vector: \( \nabla f_1 = \langle 2x, 2y, 2z \rangle\)

Surface 2: \(x + y - z = 3\)
Gradient vector: \( \nabla f_2 = \langle 1, 1, -1 \rangle\)

Ab humein point (2, -1, 2) par in dono gradients ko calculate karna hai:

For Surface 1:
\( \nabla f_1 = \langle 2(2), 2(-1), 2(2) \rangle = \langle 4, -2, 4 \rangle \)

For Surface 2:
\( \nabla f_2 = \langle 1, 1, -1 \rangle \)

Ab humein dono vectors ke beech ka angle nikalna hai. Iske liye hum dot product ka istemal karenge:

\( \text{Dot product} = \nabla f_1 \cdot \nabla f_2 = (4)(1) + (-2)(1) + (4)(-1) = 4 - 2 - 4 = -2 \)

Angle ka formula:
\[ \cos(\theta) = \frac{\nabla f_1 \cdot \nabla f_2}{\| \nabla f_1 \| \cdot \| \nabla f_2 \|} \]

Yahaan par \( \| \nabla f_1 \| = \sqrt{4^2 + (-2)^2 + 4^2} = \sqrt{36} = 6 \) aur \( \| \nabla f_2 \| = \sqrt{1^2 + 1^2 + (-1)^2} = \sqrt{3} \)

Ab angle ka cos nikalte hain:
\[ \cos(\theta) = \frac{-2}{6 \times \sqrt{3}} = -\frac{1}{3} \]

Angle ka value negative hai, kyunki dot product negative hai, jo indicate karta hai ki vectors ke beech ka angle obtuse hai.

Ab hum angle ka value nikal sakte hain:
\[ \theta = \cos^{-1}(-\frac{1}{3}) \]

Calculator mein iska value find karke angle ka approximate value mil jayega.

[AnahitaGull-orsw]

Hi everyone
plz is book ki pdf or notes share kar da ya book name

[nikhilboddula]

thapu dengindhi sum eppudoo grad O2 dhagara

[Kk_]

3:41 yaha z to hai hi nhi to z ki value kyo rakhinge 🤔🤔 ???

[Thxhtn]

Didi apka rota avaj suneke mujhe rona aara 🥲🥲

[ShivaniIngleOfficial]

Sorry, but apka answer galat aagya the right answer is cos inverse 8/3√21 i.e theta equal to 54.415 degree.
For proof you may google it