SF.dr where F Cxpy;Z)=y and C is the urve of intersection of yz=2 antd th 4he sylinder x?ayL with the plane counter- clock wise rotation a) What is.the formitatasisociated wih Stokes' T torp bi Which sidetof the formülashould Twe dese if we are asedito eraruate? s Fidr taq with? Stokes Theorem? ☺ vsë Stokes' Theorem to evaluake S Fid

Q: Find Sdr where C is a circle of radius 3 in the plane x+y+ z = 5, centered at (2,1,2) and oriented…

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Q: Find parametric equation of line-t- y + 3z = 23 Hence find its intersection with plane 2x +

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Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

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Q: 2. Find the distance between the line with parametric equations ï = 1 + 2t, y = −2+ 4t, z = 4 − 4t…

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Q: 8. ( Determine whether the following two planes are intersect or not. If they intersect, find the…

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Q: QUESTION 1 If s is a dlosed, piecewise-smooth, orientable surface, which of the following…

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Q: Use trapezoid GHIJ to answer the following questions. Ay G(O, 3) H(2,3) j(-1, 1) /(3, 1)

A: Given , trapezoid whose coordinates are  G(0 , 3) ; H(2 , 3) ; I(3 ,1) ; J(-1 , 1) (b) Given , the…

Q: In the dogram B,cand O lie in the same honzentai plane and AB IS verical to the plane. AD = 2p and…

A: Concept of Cosine rule is required to solve this problem.

Q: I Find the Parametric equ. sor he line f intersect of Pae Plan 3X- 6y -22 =15 and 2x+Y 2Z%=5? X-3…

A: 3x-6y-2z=152x+y-2z=5a→=3, -6, -2b→=2,  1, -2a→×b→=ijk3-6-221-2a→×b→=(12+2) i^-(-6+4) j^+(3+12)…

Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: (b) Starting by finding a single vector function that represents the intersections of the surfaces…

Q: Find the distance from the point S(5, -9,6) to the plane 2x+ 10y + 11z = -10 4. O A. 225 52 B. 5 4…

A: Given:  S(5,-9,6)  And equation of plane is  2x+10y+11z+10=0

Q: eraluate (F di in hoc x y 2. where is me curue an Plane pom (0,0)

A: Formula Used:-∫CF→.dr→=∫abF→(r→(t)).r'(t)dtfor a≤t≤b

Q: U. R. S. V. P.

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Q: The plane equation that has 2.5 units distance to the plane 5x- 2y + 3z = 4 is %3D O a.…

A: Option (d) is correct.

Q: Cartesian equation of the curve given by the equation in polar coordinates ? O A) y= v3x O B) x =…

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Q: Name the transformation that maps figure T onto the correct T',T", T"" T" T' T T"" Drag the boxes to…

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Q: Which of the following tessellates the plane? (Circle all that apply.)

A: We have to find out from the given figure which is tessellates the plane.

Q: Which of the following statement(s) is/are true? O A. The plane y + 2z – 9 = 0 is perpendicular to…

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Q: Suppose we have: u = and v = . Based on their relative positions in the xy-plane, in which…

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Q: You are given the parametric equations ¤ = 10 – t², y=t³ – 12t. (a) List all of the points (x, y)…

A: Slope of tangent line is given by:

Q: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

Q: The parametric equations represented by x = secß, y = tanß, - T/2 < B< T/2 is a: A. Circle B.…

A: Given x=secβ  and y=tanβ

Q: let an intersect is movig 1311 along the graph of the. Para metvic eqvation Which is given by and y…

A: We have to first convert polar to Cartesian coordinates.

Q: Find the parametric equa

A: Given, the line in ℝ3 containing the points P=(-2, 5, 4)  and Q=(-4, 1, 1).

Q: Which of the given lines is parallel to the line L defined by the parametric equations below? L:…

A: Given line is  L: x = 8+t , y = -4 +2t , z = -5t we have to check which of the given lines is…

Q: 6. Consider the points A= 0 and B = 3 on the real axis Sketch the following baricentric…

A: The baricentric coordinates are x0=12,12, x1=13,13, x2=2,-1, x3=-1,2 and x4=0,1. In general, if…

Q: Identify the surface with the given vector equation. r(0,0) = 2sinocosei +2sinosinej +2/1+sin?ok a.…

A: The minimum number of parameters needed to represent a surface is two. Therefore, in general, the…

Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: Given: The two surface equation: z = y2 and  x2 + y2 = 4

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.