In Exercises 1–8, find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. PROBLEM 8 PLEASE.8. r(t) = (t sin t + cos t)i + (t cos t - sin t)j, In Exercises 1-8, find the curve's unit tangent vector. Also, find thelength of the indicated portion of the curve.1. r(t) = (2 cos t)i + (2 sin t)j + V5tk, 0

Answered: In Exercises 1–8, find the curve’s unit…

In Exercises 1–8, find the curve’s unit tangent vector. Also, find the length of the indicated portion of the curve. PROBLEM 8 PLEASE. 8. r(t) = (t sin t + cos t)i + (t cos t - sin t)j,

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 33E

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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.

Question

In Exercises 1–8, find the curve’s unit tangent vector. Also, find the
length of the indicated portion of the curve. PROBLEM 8 PLEASE.

8. r(t) = (t sin t + cos t)i + (t cos t - sin t)j,

In Exercises 1-8, find the curve's unit tangent vector. Also, find the
length of the indicated portion of the curve.
1. r(t) = (2 cos t)i + (2 sin t)j + V5tk, 0<t <
2. r(t) = (6 sin 2t)i + (6 cos 2t)j + 5tk, 0 <t < ™
3. r(t) = ti + (2/3)t³/2k, 0 <t< 8
4. r(t) = (2 + t)i – (t + 1)j + tk, 0 < t < 3
5. r(t) = (cos³t)j + (sin³t)k,
6. r(t) = 6r°i – 2t³j – 3ť°k, 1<t< 2
7. r(t) = (t cos t)i + (t sin t)j + (2V2/3)t³/²k, 0 <t < ™
0 <t< T/2
-
8. r(t) = (t sint + cos t)i + (t cos t – sin t)j, V2<1s2
9. Find the point on the curve
r(t) = (5 sin t)i + (5 cos t)j + 12tk
at a distance 26™ units along the curve from the point (0, 5, 0) in
the direction of increasing arc length.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

Step 1

You will say to solve the problem number 8.(8.) We will find the curve’s unit tangent vector. And the length of the indicated portion of the curve.

1. Curve : r(t) = (t sint +cost)i +(t cost- sint)j

,sqrt 2<=t<=2

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