Exercise 1.1.17. From the origin draw a line through any point P of the circle of radius a centered at (0, a). Find the intersection Q of this line with the horizontal line y = 2a. Drop a vertical line from Q and intersect it with a horizontal line passing through P. This intersection is a point on the curve known as the witch of Agnesi.' See Figure 1.10. Let t denote the angle between the vertical axis and the line through (0, 0), P and Q. Show that the witch W(t) is given in terms of t by W (t) = (2a tan t, 2a cos? t).

Exercise 1.1.17. From the origin draw a line through any point P of the circle of radius a centered at (0, a). Find the intersection Q of this line with the horizontal line y = 2a. Drop a vertical line from Q and intersect it with a horizontal line passing through P. This intersection is a point on the curve known as the witch of Agnesi.' See Figure 1.10. Let t denote the angle between the vertical axis and the line through (0, 0), P and Q. Show that the witch W(t) is given in terms of t by W (t) = (2a tan t, 2a cos? t).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 6AEXP

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Concept explainers

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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Exercise 1.1.17. From the origin draw a line through any point P of the circle of radius a centered
at (0, a). Find the intersection Q of this line with the horizontal line y = 2a. Drop a vertical line
from Q and intersect it with a horizontal line passing through P. This intersection is a point on
the curve known as the witch of Agnesi.' See Figure 1.10. Let t denote the angle between the
vertical axis and the line through (0, 0), P and Q. Show that the witch W(t) is given in terms of
t by
W(t) = (2a tan t, 2a cos? t).

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