Let (t) = (t, t, tº, tª) for all t € R. Define C = Þ(R). Let p = (1, 1, 1, 1). Derive the tangent and normal spaces to C at p; that is calculate TpC and NpC. You may describe ToC and NpC as a span or as point-sets in R4 given by cartesian equations, your choice.

Q: Q.7: find the directional parametrization of the line segment joining two point A(2,1,3) and…

A: It is a basic questions of 3-D geometry , we have equate the equation only

Q: 02. segment (1,1,0) and C₂ is the curve parametrized by R(t) = (e²t + t²,e¹, t), t = [0,1]. (a) Find…

A: Given: F→x,y,z=ez-y,x-z2,y3 and R→t=e2t+t2,et,t, t∈0,1 We have to find the work done by F→

Q: Let (x, y) eRx R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and s(x, y)) =…

A: This is a problem of multivariable Calculus.

Q: Let V be an n-dimensional vector space. Define f : V \rightarrow \R by f(v) = |v2|. Let p,q \in V.…

A:

Q: =urface at the given point. y? at the point (3, 2, 2) 9.

A:

Q: Consider the points P = (1,2,0), Q = (0,1,2), and R=(2,0,1). Let A be an arbitrary point in…

A:

Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…

A:

Q: EXERCISE 4.4 Given P₁ = (-1, −1, 0) and P₂ = (1, −1, 0), derive the parametric expression (P(u, 0))…

A:

Q: Let L₁ be the line parametrized by (4-2t, 2-t, 3+t). Let L₂ be the line parallel to L₁ going through…

A:

Q: Given is the plane V : a · x = 9 with a = (2, -3,6)t. Calculate the distance from O= (0,0,0) and…

A: Given that:The Plane  with To find: The distance from  and  to V.Concept:The distance d between a…

Q: Sketch a contour map and graph of . a. g(x, y) = 9x² + 4y² b. z = y/x

A: The given function is: g(x, y) = 9x2 + 4y2 The contour map of the above function is:

Q: Find the equation for the tangent plane to the surface -3x+ 9y -7z = -26 at the point (1,-1, Lütfen…

A:

Q: Let V₁ = -4 1 | -12 B-B- V2 = 4 -3 11 -5 " and y = For what value of h is y in the plane spanned by…

A: and We have to find the value of .

Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 36 r(t)

A: Represent the plane curve by a vector- valued function                       x2 + y2 =…

Q: Match the space curves in the figure below with the following vector-valued functions: O A. r(t) =…

A: See that options ,  A )  r ( t ) = < 1 , t , t >  If we consider the first two coordinates ,…

Q: Let P(-4, 1, -3) be a point that is not on the line L . Let the line L pass-through points Q and R…

A:

Q: ind an equation of the tangent plane at P = ( 2,3, - 3 |to the given surface. 10x? + z?e"-* = 49…

A:

Q: a. Find vectors nį and n2 that are normals to II and IL respectively and explain how you can tell…

A: The planes are given by π1: x1x2x3=0-33+λ11-12+λ2313 and π2: x1x2x3=000+μ112-1+μ2340. For π1:…

Q: %3D Find the angle of intersection between the curves xy +y =1 and y = (x+ 1)- O 87.96 degrees 69.78…

A: