Given f(x.y.:)=9x² – 5:-7+xy and Vf = (18x+ y,x,-5). Find a unit %3D normal vector at point P = (1,0, 1).

Q: Find a vector function that represents the curve of intersection of the paraboloid z = 5x² + 2y² and…

A: The paraboloid z=5x2+2y2 and the cylinder y=3x2. We have to find a vector function that represents…

Q: State the theorem for Gradient as a Normal Vector.

A: State the theorem for Gradient as a Normal Vector.

Q: 6. Find a vector which is normal to the currive: 3= 11 at (1,2). x³ + xy + y²

A: We have to find a vector which is normal to the curve: x³ + xy + y³ = 11 at (1,2).

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

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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: e vector equation ū=

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Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

Q: 5. Consider the curve whose equation is (x² + y²)² = 9 (x² - y²). Find a normal vector and a tangent…

A: First we find partial derivatives of f(x,y) w.r.t x and y. Then find general tangent vector normal…

Q: (b) part of parabola y = −2x² from (−1, −2) to (2, —–8)

A: Given Equation of parabola y=-2x2 from -1, -2 to 2, -8.

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: For the function f(x, y) (5,-4) that has a positive Question Help: D Video -4-2²-² 1 component. find…

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Q: [1 [4] Determine if the vectors v₁ = 2, 12 vi 2,√2 = 5, and v3 L3. L6. independent. = 8 are linearly…

A: Step 1:The provided vectors are:v1​​=⎣⎢⎡​123​⎦⎥⎤​,v2​​=⎣⎢⎡​456​⎦⎥⎤​,v3​​=⎣⎢⎡​789​⎦⎥⎤​It is needed to…

Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: 5. [6.1] If vector ā reaches from the origin to point (5, –7), determine the magnitude of ā.

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Q: If the position vector r(t)=e9t i +9sqrt(2)t j + e-9t k, compute the normal component of the…

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Q: Plots the given vectors on a normal chart with logarithmic x axis and linear y axis,…

A: See the attachment

Q: Q1. If the components of a contravariant vector in (x') coordinate system are (3,4). Find its…

A: 1) Given information: x¯1 = 7x1 - 5x2x¯2 = -5x1 + 4x2 The components of contravariant in xi…