find the tangent line to the vector function at the given point. 7(t) - cos (4 t) i+3sin(4t)j+tR at t=n 7(t) = 1. 12 t .(n. 3 m2t) R None 7(t) = 2nỉ + 12nt j+ 3m t k %3D

Q: PARAMETRIZED, VECTOR, VECTORS, MULTIVARIABLE CALCULUS NEED ALL WORK SHOWN CLEARLY AND ANSWERS

A: Given: r(t) = <3e^3t, sint, 3t^2-6t>

Q: t3 Find the vector equation of the tangent line to 7(t) = 2 (e1-t) In t i+ tan-1 tj+ k at cos(t n)…

A:

Q: If an object follows the path of the two-dimensional vector-valued function p(t)=(16−cos(t),…

A: Given p(t)=(16−cos(t), 0.6πt−0.15t2−3)

Q: Find the unit tangent vector for the vector function : r(t) = (t2 + 1,3 t, t3> %3D (1+4t2+9t)3…

A:

Q: 13. r(t) = ei+e j+4k at t 0

A: Given vector :

Q: 4. Let r(t) = (t)i + (t-16t²) ; be the position of a particle in a plane at time t. Find the angle…

A:

Q: 2. For the vector-valued functions given by 7(t) = i- j+ In t k and ü(t) = t?i – 2tĵ + k Find

A:

Q: Find the derivative of the vector function r(t) = In(18 – 12) i+ v5+tj- 9e“ k r' (t) = (

A:

Q: (1) Find the domain of the vector-valued functions: (a) (t) = (t-, (t+1)-1, sin¬' (t)} (b) F(t) =…

A: To Determine: find the domain of the vector-valued function Given: we have given two functions…

Q: The monkey saddle z = x³ - 3xy² can be intersected with the cylinder x² + y² = 1 to produce the…

A: Given monkey saddle is z=x3-3xy2 and the cylinder is x2+y2=1. The given curve is the intersection of…

Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: Suppose that a particle follows the path r(t) = 2 cos(3t)i+ jsin(3r) – ť² k. Determine the velocity…

A:

Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = 4 sin…

A: Given position vector is                                        r(t)=4sint i-4cost j+tant k tangent…

Q: Given the vector-valued functions ü(t) = e-5ti + e'; – 4tk v(t) = 5ti + 5t?j – 3k d find (u(t) ·…

A: Given vectors u→(t)=e-5ti+etj-4tkv→(t)=5ti+5t2j-3k

Q: Suppose a projectile is launched at an angle of 60 above the horizontal. If the initial speed of the…

A: Topic - components Of vector

Q: 3. Find the unit tangent vector at t = T/2 for the following parametrized curve: F(t) = (cos 2t, 4,…

A: The given parametrized curve r→(t)=cos2t, 4, sin2t

Q: b) Find the unit tangent vector of 7(t) = (t? – 1)î + t²j at t = 2.

A: We have to find the unit tangent vector.

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

A:

Q: 3. (a) Given the vector valued function r(t) = 4cos nti + 4 sin ntj + tk. Find the position vector,…

A:

Q: 5. Consider the vector function F(t) = (9 – - 2t, 4+ 2t, v2t² ) (a) Find the arc length of the curve…

A: Solution is here

Q: x-1 y-2 z-1 2 -6 7 1 F(t) = ( 21 + ¹ )i + ¹/ (m² − 3)} j + t√21³-1k at t=1 1 4 (c) show that the…

A:

Q: Find the unit tangent vector for the vector function : r(t) = (t? + 1,3 - t, t) (1+4t2+9t)3 1+4t?+9t…

A: The derivative of a vector valued function gives a new vector valued function that is tangent to the…

Q: Find the unit tangent vector of the given curve. r(t) = (7- 2t)i + (2t - 3)j + (6 + t)k 2 1 O A.…

A:

Q: 5. Consider the vector function F(t) = (9 – 2t, 4 + 2t, /2t² ) (a) Find the arc length of the curve…

A: Given that r→t=9-2t,4+2t,2t2. (a) The objective is to find an arc length of the curve on 0≤t≤1. The…

Q: Find the unit tangent vector at the indicated point of the vector function r(t)=e^(3t)cos(t)(i) +…

A: Given vector is,

Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

A:

Q: b) Find the unit tangent vector for.. r(t) = at t=0

A: The unit tangent vector can be calculated using the formula T→(t)=r→′(t)‖r→′(t)‖. The denominator is…

Q: Consider the vector-valued function r(t) = (t2− 2)i + sin-1(t)j +1/(1 + t)k Find parametric…

A: Here, the given vector-valued function is: r(t)=(t2-2) i+sin-1(t) j+11+tk To find the parametric…

Q: Given that the acceleration vector is a (t) -9 cos(-3t), -9 sin(-3t), 5t), the initial velocity is…

A:

Q: Find the domain of the following vector functions: a) r(t) = e-3ti + v4 – t²j + ln(t – 1) k t-2 b)…

A: given vector function

Q: x-1_y-2_z-1 -6 (c) show that the line 2 7 curve F(t) = (21+²) 1+ ²+ (in ²²-3) 1+1√21³²-1k at 1=1 i+…

A:

Q: B. Given that r (t) = (3t cos t) j - (3t sint) k , is the position vector of a moving particle, find…

A:

Q: 3. (a) Given the vector valued function r(t) 4 cos nti + 4 sin ntj + tk. Find the position vector,…

A: Since you have sent 3 different questions therefore according to the guidelines we are bound to…

Q: t3 Find the vector equation of the tangent line to 7(t) = 2 (e1-t) In t i+ tan-1 tj+ k at cos(t t)…

A:

Q: 13. The position vector of a particle at time t is R = cos (t – 1) i + sinh (t – 1) j+ atk. If at t…

A: Given that  The acceleration and position of a particle are perpendicular to each other . To find:…

Q: 1. Given the vector-valued for R(t) = (2 sin 2t-1)i+ 2 cos 2tj+ 3tk. %3D (a) Find the length of the…

A: Given that Rt=2sin2t−1i+2cos2tj+3tk

Q: Find the tangent, normal, and binormal vector functions for the following three curves:   1:…

A: We have to find the tangent vector, normal vector and bionomial vector function

Q: Find a tangent vector at t= In 2 for the following parameterized curve. r(t) = 5 e'i+e -2tj+6 e 2k…

A: Explanation of the answer is as follows

Q: 1. Find the unit tangent vector to r(t) = at t = n.

A:

Q: 1. Find the tangent vector to the curve 6t r(t) = [t³ – t, t+1 , (2t + 1)*] at t = 1.

A: As per our guidelines we are supposed to answer only one question. If you want solution of any…

Q: 6. Consider the vector-valued function f: R → R³ given by: f(t) = t/ 4t2 + 1, sin(t) cos²(t), for t…

A: a) f(t)=t4t2+1,sintcos2t,2t2+1we know that f(t)=f1,f2,f3⇒f'(t)=f'1,f'2,f'3hence…

Q: 1. (a) Given the scalar function g(x, y, z) = (1+x³) sin z+e cos y, calculate v = Vg and find V ·v.…

A:

Q: a) Let 1 cos t i+ sint j - 4 k. 4 r(t) = be a vector function. i. Sketch the vector function r for 0…

A:

Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (2 -…

A:

Q: Compute the tangential and normal components and express the acceleration a in the form a= arT+aŋN…

A: Calculate the value for aT using the derivative.…

Q: 3. For the motion vector r(t) = ti+ In (cos t) j, find (i) The velocity (ii) The speed at t=N Write…

A:

Q: 1. Find the tangent vector to the curve 6t r(t) = [t° – t, (2t + 1)*] at t = 1.

A:

Q: Find the derivative of the vector function r(t) = In(5 – t²)i+/16 +tj+ 7e 8t k r'(t) = (

A: Given vector valued function is rt=ln5-t2i+16+tj+7e-8tk

Q: C) If R(t) = (In(t2 + 1)i + (tan-t)j + (VE +1)k, is the position vector of a particle at time (t).…

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.