Exercise. A curve C in space is described by the vector-valued function: p(t) = (t – 1, 2t, 2t? + 2) Find a unit vector with positive x-component that is orthogonal to both p(0) and p'(0): Previous Next

Q: 1. Use the parameter r =t to find a vector-valued function for the space curve represented by the…

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Q: Find the domain of the vector function 7(t) = (v4 – t², e-3t, ln(t + 1)

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Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

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Q: 1) The domain of the vector position r(t) = 1+2 i+ sintj+ In(9- t²) k

A: We are entitled to solve only 1 question at a time so, I am providing you the solution of the first…

Q: Find all values of t for which the tangent line to the curve r(t) = (2t – t,t - t²) is orthogonal to…

A: Find the solution below

Q: QUESTION 10 Let r(t)=(1-t2, 5t, 2t3). Find the z-component of the vector r'(4).

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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: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t y…

A: Given, The parametric equation of the line D passing through A and parallel to vector v is  x =…

Q: Q1:- Find the domain of the following vector functions:- (a) f(t) = (cos nt)i – Ln(t)j + vt – 2k %3D

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Q: At which point P does the curve r(t) =( 2t2, 4t+1, t³ ) given in vector form have the tangent vector…

A: Given, r(t)→=2t2,4t+1,t3  tangent vector 4,4,3 we know derivative of vector valued function gives…

Q: Find the Wronskian of the following vector functions: 3t-1 -t+1 u (t) = -t v (t) = 3t

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Q: A vector A-xyzi+3x'yj+ (xz-y'z) k.

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Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: Given the operator S on the vector space R₁ [x] given by S (a+bx) = -a+b+ (at 2b) x A) What is SC1)…

A: We know that Pn is the vector space of all the polynomials of degree n+1 and the basis for this…

Q: show that the given vector functions are linearly independent on (−∞,∞).

A: We need to show that the given vectors are linearly independent on -∞,∞ x1t=t+1t-12t,…

Q: Prove that the vector T′(t) is 0 for an object moving in a straight line.

A: Here an object moving in a straight line. The path of the object can be given as follows.…

Q: (a) Consider the curve C : r(t) = [t , –t², 2– t²]. Find a tangent vector, a unit tangent vector and…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Show that the vector form (x, y, z) = (-5, 1,0) + t(3,2, 1) for some parameter t ER satisfies the…

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Q: 5) Consider the vector function r = (9 – 2t, 4 + 2t, vZt²) a. Find the length of the path on 0<t<1.…

A: Given vector function The length of the path is found by the formula Given interval is 0 to 1

Q: 4 If r(t) =(1+t)3/2i+(1 - t)/2j + tk, t= 0 then the binormal vector B is

A: Consider the position vector,   rt=491+t32i+491-t32j+13tk,   t=0                      Orrt=491+t32,…

Q: Find all values of t for which the tangent line to the curve r(t) = (3t – t°,t –- t²) is orthogonal…

A: Given curve is

Q: EXERCISE 2.1 Derive the expression of the normal vector K(t) of the parametric curve P(t) = (−1,…

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: Consider the vector-valued function Ř(t) with R'(t) = (sec²(t – 1), , -2). (a) Find Ř(t) given Ř(1)…

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Q: Find the vectors T and N and the binormal vector B=TXN, for the vector valued function r(t) at the…

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Q: 1. The acceleration of an object is a=2i+4j+6k.  Compute the position vector r(t) if the object at…

A: a=double derivative of position vector

Q: At which point P does the curve r(t) = ( 2t2, 4t +1, t³ ) given in vector form have the tangent…

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Q: 1 (b) Find the span of vectors i = |0 and j = |1 in R3

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Q: H.W 3- Find a vector V =xi +yj +k that is orthogonal to both A = 3i + j +k _and B = 3i +2j +2k .

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Q: Find a vector function r(t) that satisfies r′′(t) = [6t, −2t−1/2, 1], r′(1) = [0,1,0],and r(1) =…

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Q: Find the vectors T and N and the binormal vector B = T x N, for the vector-valued function r(t) at…

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Q: Consider an object following the path of the two-dimensional vector-valued function p(t) = (2t? – 2t…

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Q: Find a vector function that satisfies the conditions r"(t) = 12ti – 31-/2j+2k, r'(1) = j, r(1) = 2i…

A: We have to find a vector function that satisfies the conditions…

Q: Find the domain of the vector function 7(t) = (, V1-t, 1 1 – t, t t +1 A. (-0, –1) U (-1,1) В. (1,…

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Q: Given r(t) be the vector function that describes the curve of intersection between the cylinder…

A: First, parametrize the cylinder equation to get x(t) and y(t) and then find find z(t) from the…

Q: With T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whethe x is…

A: Given  A=10-3-3162-2-1, b=-23-1

Q: For the vector valued function given by 7(t) = (,-1, In t) and u(t) = (t²,-2t, 1) find %3D %3D…

A: Given that r→t=1t, -1, ln t and u→t=t2, -2t, 1 We can write the given vector as r→t=1ti +-1j+ ln tk…

Q: A. Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1…

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Q: Substituting t=0 for the inital equation qoul get &lt;-1,02&gt;, and again with the derivative foem,…

A: Given

Q: Consider the vector-valued function F(2,) = [xy² + 2ye* х, у y 3xe-y Which of the following are NOT…

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Q: Consider the curve F(1)=i +(/2 In(?))j + 1 -k. | а) Find the binormal vector B(1)

A: Given the curve  r→(t) = i→ + 2ln(t)j→ + 1tk→

Q: (b) Let r(t)-ti- +(4-t) k, then the vector equation of the line tangent to the graph of r(e) at the…

A: Given:- r(t) =t2 i -(1+t)-1j +(4-t2)k To find:- Vector Equation of tangent line passing through…

Q: 1) Find a vector function r(t) that represents the intersection of the surfaces: = /x² + y² z = y +…

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Q: The smooth vector-valued function P(t) satisfies P(2)= (−4, 8,−7), P′(2)= (0,-5,2), and P’’(2)= (3,…

A: As per company guidelines i am solving first question please resubmit the question for next one…

Q: Question 3 Find a vector-valued function, using the given parameter, to represent the intersection…

A: We need to find r(t).

Q: In exercises 1–18, sketch the curve traced out by the given vector- valued function by hand. 1. r(t)…

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Q: A smooth curve C is defined by some vector function R(t) with R (7) 2 = = (π,0,−2) and R' (t) = (2,…

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Q: Find the vectors T and N and the binormal vector B = T × N for the vector-valued function r(t) = ti…

A: first, we will differentiate the vector r(t) we get  r'(t)=i+2tj+t2k doing the modulus we get…

Q: 14. Given F(1) = (-1,3,0) F'(1) = (2,–2, 1) F"(1) = (0,–1, 4), What %3D is the vector equation of…

A: We will use basic vector calculus here to solve this question.