Question

Find parametric equations for the line through $P_{1}$ and $P_{2}$ and also for the line segment joining those points. (a) $P_{1}(3,-2), P_{2}(5,1)$ (b) $P_{1}(5,-2,1), P_{2}(2,4,2)$

Name: Problem 3, Chapter 13: Calculus A New Horizon
Uploaded: 2021-07-08T00:13:26-08:00
Duration: 3 min 22 s
Channel: Melvin Adkins
Description: Find parametric equations for the line through P1 and P2 and also for the line segment joining those points. (a) P1(3,-2), P2(5,1) (b) P1(5,-2,1), P2(2,4,2)

   Find parametric equations for the line through $P_{1}$ and $P_{2}$ and also for the line segment joining those points.
(a) $P_{1}(3,-2), P_{2}(5,1)$
(b) $P_{1}(5,-2,1), P_{2}(2,4,2)$

Calculus A New Horizon

Howard Anton 6th Edition

Chapter 13, Problem 3

Instant Answer

Solved by Expert Melvin Adkins

07/08/2021

Step 1

This vector can be found by subtracting the coordinates of $P_{1}$ from the coordinates of $P_{2}$. For part (a), the vector is given by $P_{2} - P_{1} = (5-3, 1-(-2)) = (2, 3)$. For part (b), the vector is given by $P_{2} - P_{1} = (2-5, 4-(-2), 2-1) = (-3, 6, Show more…

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Find parametric equations for the line through $P_{1}$ and $P_{2}$ and also for the line segment joining those points. (a) $P_{1}(3,-2), P_{2}(5,1)$ (b) $P_{1}(5,-2,1), P_{2}(2,4,2)$

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Key Concepts

Parametric Equations

Parametric equations express the coordinates of points on a line as functions of one or more variables (parameters). This method features an initial point and a direction vector, allowing the description of every point along the line via an equation that combines these elements.

Direction Vectors

A direction vector indicates the orientation of a line in space and is obtained by subtracting the coordinates of one point from another. It serves as the 'driving force' in the parametric representation, showing how to move from one point to any other along the line.

Line Segment Parameterization

Line segment parameterization involves the formulation of parametric equations with a restricted parameter domain, often the interval [0, 1]. This ensures that the equations only represent the finite part of the line that connects the two endpoints.

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