A normal vector to the tangent plane for the surface z = , at the point (1, 1, 1) is: y - Select one: O (1,-1, 1) O (-1,1, –1) O (1, 1, 1) O None of them O (-1,1, 1)

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

A:

Q: Given w f(z,y, 2) = zy²z. Find: Ograd/(1,3,-2) 3. (b) equation of the tangent plane to the surface…

A:

Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

A:

Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

A:

Q: Sketch the curve with the given vector equation by finding the following points. r(t) = (t, 3 t, 2t)…

A: Given : r(t) = { t, 3 - t, 2t}

Q: Consider the surface of equation z = x2 + y² . What is the equation for the tangent line to S at the…

A: We need to find equation of tangent line.

Q: Show that this curve y represents the vector (1,0) as v = 1- +0- in the sense that, for an arbitrary…

A: Given that γ(t)=(t,t2)in R2, t∈[-1,1] The objective is to show that curve represents the vector…

Q: A normal vector to the tangent plane for the at the point (1, 1, 1) is: y surface x =

A: A(1, 1, 1)z= xyf(x,y,z) =xy-zfx=yfy=xfz=-1Normal vector to the tangent plane for the surface;n^…

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: Let C, be a curve defined by some vector function R with unit binormal B such that 3 Ř(0) = (-2,5,…

A: For calculating the osculating plane we use the fact that the binormal is also the normal to the…

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

A:

Q: Let P be the tangent plane to the surface z-2x2+y2 at the point Q=(1,1,3). Which of the following…

A: Tangent plane to given surface

Q: Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a…

A: Given- Let S be the surface obtained by revolving the plane curve 2x = 9 - y2 about the y-axis. To…

Q: Where does the plane tangent to z = At z = 5exy at (7, 7, 5) meet the z-axis?

A: We find equation of tangent plane to z=5e^(x-y) at (7,7,5)

Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

A: For tangent plane of the surface f(x,y,z)=k at a given point normal vector to tangent plane  will be…

Q: Consider the following function. T: R? - R, T(x, y) = (2x?, 3xy, y²) Find the following images for…

A:

Q: Let S be the surface described by the vector function Ř(u, v) = (v², u + v, e²«). Find an equation…

A:

Q: y Consider the surface of equation z = X+Y² What is the equation for the tangent line to S at the…

A: This is a problem of vector calculus.

Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: Write formulas for the unit normal and binormal vectors of a smooth space curve r(t)

A: The formulas for unit normal vector  and binomial vectors of a smooth space curve r(t).

Q: True or False: The vector (10, 2, –4) is normal to the surface x2 + y? – 22 = 22 at the point P =…

A:

Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

Q: 8. A line initiated from (1,0,2) and parallel to a vector i+j+k what is the parametric equation of…

A: we have to find equation of line in 8.

Q: Find a parametrization r(t,s) for the plane which contains the point P(-9, 7, 1) and the line…

A: Use plane concept