Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent plane. n = P

Q: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

Q: Find the open interval(s) on which the curve given by the vectorvalued function r( ) = 2 cos3 i + 3…

A: Consider the given vector-valued function: Here the objective is to find the open intervals on…

Q: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: /Find the tangent and normal vector for curve r= (5sin n i+5 cos n j+n k) n=(In 2t)

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Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and…

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2,…

Q: Find the directional derivative of the function f (x, Y, z) = 6x² –- 2xy + yz in the direction of…

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Q: Sketch the level curve corresponding to c = 0 for the function given by           f(x, y) = y − sin…

A: We have given the function; f(x, y) = y − sin x This can be written as; z=y − sin x

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve 7(t)…

A: We will find out the required value.

Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j, 0<t…

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Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: Consider the curve defined as r(t) = e^ti + e^tj + t k Determine the point on the curve where the…

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Q: Find a normal vector at point P. xy2 - 4x2 + y + 8x = 7, P(4, 3) Find a tangent vector at point P.

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve F(t)…

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Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

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Q: 2. Find the equation of the normal line and the tangent to the parametric surface defined by the…

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Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: Find the equation of the tangent line of the vector function F(t) = (e= cos(t), e=' sin(t), e') at…

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Q: A particle is moving along the curve whose position vector is given: R(t) = (cost + tsint)i + (sint…

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 3, 11) for the function…

A: The unit vector normal to the surface f(x, y, z)=0 is ∇f∇f. where ∇f = fx, fy, fz and ∇f = fx2 + fy2…

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve r(t)…

A: This question can be solved using the concept of vectors and derivatives.

Q: Find equations of the normal line and the tangent plane to the parametric surface defined by the…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  compare coordinate on…

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

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Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by &lt; t^2+1, ln(2t+3) &gt; for all t&gt;=0

Q: Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the…

A: To find: The normal vector of the tangent plane to the surface at the given point. Given…

Q: Q1:(A) What is the angle between the normal vectors to the curve F (1) = (2x² + x + 1)i + (+1)j +rk…

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

A: As ∇f is the gradient of the surface f , it will point towards the normal vector of the surface.

Q: 3x2 – 4y2 at which the vector 11. Find the points on the graph of z = (3, 2, 2) is normal to the…

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Q: Find a unit normal vector to the surface at the given point. x²y3 - y?z + 2xz3 = 4 (-1,1, –1)

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: For the function f(x, y) = 3x – 5xy + 4y – x + 4y – 2, find a unit tangent vector to the level curve…

A: Gradient of  function: Let z=f(x,y)z=f(x,y) be a function such that  partial derivating of with…

Q: e the electric flux through a paraboloid z = x² + y² – 16 that lies . It is oriented by an outward…

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Q: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a(7 - cos 0) and = 6, where…

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: Here we use the concept of gradient of a scalar function at given point.

Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Find a vector n normal to the plane with the equation x+6y + 4z = -10. n= 00> (1₂)

A: Concept: The equation of the plane is written as: ax-x0+b(y-y0)+c(z-z0)=0 or ax+by+cz=d Here the…

Q: find the tangent line to the vector function at the given point. 7(t) - cos (4 t) i+3sin(4t)j+tR at…

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Q: Find the unit tangent, normal and binormal vectors T, N and B for the curve at the point (0, 7, -1).

A: The curve is defined by the vector function rt=sint2,t2,cost2 on the domain [0,∞) To find the unit…

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

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Q: ind a formula for a vector normal to the plane tangent to f(x,y) at (xo, Yo).

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Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

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Q: The unit tangent vector of the function ⟨2t+1,(3t+1)^2,(2t+1)^3⟩ at the point with parameter value…

A: Topic - vectors Option d

Q: Find the directional derivative of the function f(x, y) = In(at + y) at the point (- 1, - 2) in the…

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Q: Find the tangent vector of r(t) = (t° , 3tª) at time t = 1. A) (3, 12) B) 15 C) (3, 7) D) 3t2 + 12t3

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