Q1:(A) What is the angle between the normal vectors to the curve F (1) = (2x² + x + 1)i + (+1)j +rk at the points (1,1,0) and (4,2,1)

Q: X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the…

A: Directional derivative of the function

Q: Express the vector == 7= Z+ y. -22] 10 as a linear combination of = -(-3) and y=

A: Consider the vector v→=-2210. To express it as linear combination of vectors x→=-4-5 and y→=1-5.…

Q: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: 6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of…

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Q: Q2) Find T N „B of the vectors the curve r(t) = at the point (1, ,1)

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Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

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Q: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

Q: Q2) Find the vectors the curve r(t) = at the point (11) of

A: First of all find r'(t) and the length of r'(t). Here, r'(t)=<2t,2t2,1> |r'(t)|=4t2+4t4+1…

Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

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Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: In this question , we have to find out velocity vector, speed and accleration vector from position…

Q: Consider the following function and point F f(x, y) = /E (a) Find the unit vectors in the direction…

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Q: Let r(t)= (212-t,t³ +1²-5t), -2≤t≤ 2. (a) Sketch the curve which is generated by r(t). You may use…

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Q: the space curve (t) = (2t, t², 2t)

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Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Q: Find a vector n normal to the plane with the equation 6z - n = (-5, (5x + 5y) = -1. >

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