Find all points of intersection of the graphs of the two equations ( y + 1)2 = x, y = x3 − 1 , (a) find the unit tangent vectors to each curve at their points of intersection, and (b) find the angles (0° 90°) between the curves at their points of intersection

Find all points of intersection of the graphs of the two equations ( y + 1)2 = x, y = x3 − 1 , (a) find the unit tangent vectors to each curve at their points of intersection, and (b) find the angles (0° 90°) between the curves at their points of intersection

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 27E

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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.

Question

Find all points of intersection of the graphs of the two equations ( y + 1)² = x, y = x³ − 1 , (a) find the unit tangent vectors to each curve at their points of intersection, and (b) find the angles (0° 90°) between the curves at their points of intersection

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.

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