Find parametric (or vector) and symmetric equations of the line which pass throughthe points P, (1,4,6) and P, (2,–1,3).

Answered: Find parametric (or vector) and…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.CT: Chapter Test

Problem 8CT

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Question

Find parametric (or vector) and symmetric equations of the line which pass through
the points P, (1,4,6) and P, (2,–1,3).

Expert Solution

Given points are,

$P_{1} (1, 4, 6) & P_{2} (2, - 1, 3)$ .

Vector equation of a line passing through two points with position vectors $\vec{a} & \vec{b}$ is $\vec{r} = \vec{a} + λ (\vec{b} - \vec{a}), λ \in R .$

And symmetric equation is $\frac{x - x_{1}}{x_{2} - x_{1}} = \frac{y - y_{1}}{y_{2} - y_{1}} = \frac{z - z_{1}}{z_{2} - z_{1}}$

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