Use the Divergence Theorem to evaluate (4x + 3y + z) dS where S is the sphere x2 + y2 + z2 = 1.

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: What does 2x + y = 4 represent in the xy plane and what in the space?

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Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: Use the Divergence Theorem to evaluate (4x + 9y + z2) ds where S is the sphere x2 + y2 + z? = 1.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

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Q: Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y +…

A: We will use equation of sphere passing through sphere S  and plane P  S+λP =0

Q: Is a subset of the plane {(x1, x2); x1 > 0, x1x2 ≥ 1} convex? Justify.

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Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: Suppose C is the line y = 5-2x in the xy-plane. Determine parametric and Cartesian equations of the…

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

Q: Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

A: The given equation of the surface is x2 + 2y2 + z2 - 4x + 4y - 2z + 3 = 0.The general equation,…

Q: The point of the sphere with equation X x²-2x +y²-4y +z²-6z+10=0 nearest to the xz-plane is 0.

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Q: urface of the spher lue of dydz + (y + z)d

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Q: Evaluate JJ (² where o is the first-octant portion of the plane 2x + y + 2z = 6 (x² + 2yz)dS

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Q: Find a parametric representation for the surface. the part of the sphere x² + y² + z² = 4 that lies…

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Q: What is the center of the sphere given by the equation x² − 6x + y² − 2y + z² + 8z + 17 = 0? -…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.