Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent plane. P =

Q: find a unit normal vector UN to the curve y = x at the point p(1,3)?

A: The given curve is y = x3, we can write it as x3 - y = 0 = f(x,y,z), where z = 0

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 unit tangent vector of the curve r=(2+t)i-(t+1)j+k

A: In this question, we need to find the unit tangent vector of the given curve.

Q: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

A: Consider the equation of the plane passing through a general point Po and with normal vector n.

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 a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

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: Sketch the curve represented by the vector-valued function                              r(t) = (t +…

A: Given: The vector-valued function  r(t) = (t + 1)i + (3t − 1)j + 2tk and it gives the orientation of…

Q: For the function f(x,y)=−5x2+2xy+3y2−x−5y+1f(x,y)=-5x2+2xy+3y2-x-5y+1, find a unit tangent vector to…

A:

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: Represent the plane curve by a vector-valued function. x- + y2 = 4 r(t) = 2 cos ti +2 sin tj

A: x2 + y2 = 4 x2 + y2 = 22 = r2 Therefore, r = 2

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

A:

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

A:

Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

A:

Q: Find the principal unit normal vector r(t) = √2ti + etj + e−tk to the curve at the specified value…

A: Given: r(t)= √2ti +  etj + e−tk at t = 0

Q: For the curve defined by r(t)=(; t³,;t²,t) calculate: The unit tangent vector, the unit normal…

A:

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

A:

Q: 10. Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j,…

A:

Q: The vector equation for the curve of intersection of the surfaces x = y² and z = y in terms of the…

A:

Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

A:

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: Let f(r.y) = r'y- Find a unit vector tangent to the level curve f(r, y) = 3 at its point (1,2).

A:

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: Compute the tangent vector to the given path. c(t) = (4t sin(t), 6t) %3D

A: The tangent vector for a vector r→t is r→'t.

Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

A:

Q: ). Determine the set Tp(Zf) of all tangent vectors to Zf at p. Is dim Tp(S) m ker d f.?

A: Sol

Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

A:

Q: Find the principal unit normal vector r(t) = ti + t2j + ln tk to the curve at the specified value of…

A: Since, our aim is to find the principal unit normal vector given below:-r(t)=t i^ + t2 j^ + ln t k^…

Q: For the function f(x, y) = 2x² – 3xy + 8y² + 2x – 4y + 4, find a tangent vector to the level curve…

A:

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

A:

Q: Find the equation of the tangent plane to z = e? + y + y² + 10 at the point (0, 5, 41). z =

A: Find equation of tangent plane from the given data

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve = (3…

A:

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: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

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: 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 unit tangent vector T and the principal unit normal vector N for the following…

A:

Q: find unit tangent vector of the given curve r(t)=(4-2t)i+(2t-3)j+(8+t^2)k

A:

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: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

A:

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

A:

Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

A:

Q: Find the tangent plane to f(1, y) = ar² + 5y² + 71²y² +9x +5y at the point (3, 6). %3D

A:

Q: Find the point on the graph of z = 3x2 – 3y? at which vector n = (48, –60, –2) is normal to the…

A:

Q: Find the unit tangent vector to the curve r(t) = (2sin(t),2cos(t)) at the points t =-n, t=0 and t…

A:

Q: (iii) Find a vector equation for the tangent line to the curve of intersection of the cylinder a² +…

A:

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