(1n |t – 1], e', vî )1. Let 7(t) =(a) Express the vector valued function in parametric form.(b) Find the domain of the function.(c) Find the first derivative of the function.(d) Find T(2).(e) Find the vector equation of the tangent line to the curve when t=2.2. Complete all parts:(a) Find the equation of the curve of intersection of the surfaces y = x? and z = x3(b) What is the name of the resulting curve of intersection?(c) Find the equation for B the unit binormal vector to the curve when t= 1.Hint: Instead of using the usual formula for B note that the unit binormal vector is orthogonal to 7 '(t) and7"(t). In fact, an alternate formula for this vector isア'(t) × ア"(t)ア(t) ×デ"(t)|B(t) =

1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b) Find the domain of the function. (c) Find the first derivative of the function. (d) Find T(2). (e) Find the vector equation of the tangent line to the curve when t=2.

1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b) Find the domain of the function. (c) Find the first derivative of the function. (d) Find T(2). (e) Find the vector equation of the tangent line to the curve when t=2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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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.

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(1n |t – 1], e', vî )
1. Let 7(t) =
(a) Express the vector valued function in parametric form.
(b) Find the domain of the function.
(c) Find the first derivative of the function.
(d) Find T(2).
(e) Find the vector equation of the tangent line to the curve when t=2.
2. Complete all parts:
(a) Find the equation of the curve of intersection of the surfaces y = x? and z = x3
(b) What is the name of the resulting curve of intersection?
(c) Find the equation for B the unit binormal vector to the curve when t= 1.
Hint: Instead of using the usual formula for B note that the unit binormal vector is orthogonal to 7 '(t) and
7"(t). In fact, an alternate formula for this vector is
ア'(t) × ア"(t)
ア(t) ×デ"(t)|
B(t) =

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