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

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: sketch the space curve and find its length over the given interval. Vector- valued function:…

A:

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

A: Let's represent the plane curve by a vector valued function.

Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

A:

Q: Sketch the space curve represented by the vectorvalued function                  r(t) = ti + (2t −…

A:

Q: Find the normal vector to plane y-x-2=0

A: A unit vector is a vector of length 1. Any nonzero vector can be divided by its length to form a…

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

A:

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: Represent the plane curve by a vector-valued function. x² = y² = 4 %3D

A: We have to represent the plane curve by a vector-valued function.…

Q: (c) Let C be a smooth curve in R³ with parameterization 7(t). Let Ñ be the unit normal vector to C.…

A: For a given smooth curve C having parametric repesentation r⇀t satisfying r'→t≠0, the unit tangent…

Q: If is a smooth curve given by a vector function r(t) a < t < b and is a constant vector, show…

A: So we have;

Q: Show that at every point on the curve r (t) = ⟨et cos t, et sin t, et⟩ the angle between the unit…

A:

Q: Find a vector parametrization of the curve x = -3z² in the xz-plane. t as the parameter in your…

A:

Q: Let C1 be a curve defined by some vector function K with unit binormal B such that 3. 3 Ř(0) = (–2,…

A: We will apply the Frenet-Serret formulas to evaluate the given problems.

Q: How do you find the length of a space curve given by a vector function r(t)

A:

Q: Sketch the space curve represented by the intersection of the surfaces           x2 + y2 + z2 = 16,…

A:

Q: Show that at every point on the curver(t) = ⟨et cos t, et sin t, et ⟩ the angle between the unit…

A:

Q: Let R be a vector function whose graph is smooth curve such that, R(2) =, R'(2) = , and R"(2) =…

A: Radius of curvature of teh function is given by formula, R = (1+y'(x)2)32y''(x)

Q: Consider an object moving according to the function from position r(t) = acoswt i + asenwt j. To…

A: As per the question we have to find the tangential and normal vector components of the path defined…

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y? = 8 and y? + 22 = 8…

A:

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: (A) Find A vector tangent and normal for the curve: x3 y = + 5 2 at the point (1, 5.5)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find a vector parametrization of the curve x=−2z^2 in the xz-plane. Use t as the parameter in your…

A: Find a vector parametrization of the curve x=−2z^2 in the xz-plane. Use t as the parameter

Q: A particle moves on a fixed surface in F.(0), which is defined by z = 2xy. During the motion, the x…

A:

Q: Sketch the curve associated with the vector function r(t) = . Hint: Show it lies on the surface z?…

A: Given the vector function is r→t=tcost,tsint,t. Skecth the curve associated with the above vector…

Q: The cone z = x² + y² and the plane z = 1 + y

A:

Q: Find a unit normal vector to the surface 6x2 + 2y2 + z2 = 225 at the point P : (5, 5, 5), and…

A:

Q: Find a vector-valued function whose graph is the indicated surface. The cylinder 9x2 + y2 = = 81…

A:

Q: Sketch and describe the curve defined by the vector-valued function below. 7(t) = (t cos t, t, tsin…

A: To sketch: The curve r(t)→=<tcost,t,tsint> Solution: Given x=tcost,y=t,z=tsint…

Q: Sketch the space curve. Vector-Valued Function r(t) = −ti + 3tj + 4tk Interval [0, 1]

A:

Q: Find a vector parametrization of the curve z = :-222 in the xz-plane. Use t as the parameter in your…

A:

Q: Let v be the blue vector drawn at point P. It is tangent to the level curve marked 7. What is Dz…

A:

Q: use the parameter x=t to find a vector-valued function for the space curve represented by the…

A: Given surface x2 + z2=4 and x - y=0   and the parameter x = t

Q: Find the unit tangent and unit normal vectors to the space curve (circular helix) determined by the…

A:

Q: Sketch the plane curve represented by the vector valued function and give the orientation of the…

A: given that r(t)=(t2+t)i+(t2-t)j

Q: Find a vector function that represents the curves of intersection of the two surfaces. 1.- The…

A:

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: 4. (a) Find the mid-point, unit tangent vector and unit normal vector at the mid-point of a planar…

A:

Q: The unit tanaent vector T and the principal unit normal vector N for the parameterzed curve 214)3D…

A: Binormal vector , B(t) = T×N Torsion for r→(t) = N'(t).B(t)

Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…

Q: write the equation of the plane passing through P with normal vector n in (a) normal form and (b)…

A: The normal form of the equation of a plane P in ℝ3 is  n.x-p = 0  or  n.x = n.p where p is a…

Q: Let R be a point in R°. Consider the plane with normal vector ñ that passes through the point P.…

A: To find the expression for the distance of a point from the pane.

Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

A: This is a question from Vector Calculus.

Q: 5. Find the unit tangent vector, the unit normal vector and the binormal vector to the curve r(t) =…

A: The given vector curve is:  r→(t)=t3,t2,t Given point is: (1, 1, 1). Therefore t = 1. Now the Unit…

Q: Find a unit normal vector to the surface f(x,

A:

Q: Sketch the plane curve represented by the vector valued function and give the orientation of the…

A: Given rt=t3i+t2j.

Q: Sketch some vectors in the vector field F(x, y) = −yi + xj.

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.