Answered: Please give as much as detail as…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 9E

See similar textbooks

Related questions

Concept explainers

Question

100%

Please give as much as detail as possible.

Find the parametric equations of the line which passes through the point (2,0,-3) in the direction of the vector v = <0,-1,5> and find the distance between the point (-3,1,-5) and this line.

Expert Solution

Step 1

$C o n s i d e r t h e g i v e n i n f o r m a t i o n . T h e g i v e n p o i n t i s (2, 0, - 3) a n d v e c t o r i s v = < 0, - 1, 5 > .$

$T h e p a r a m e t r i c e q u a t i o n i s d e f i n e d a s, \frac{x - x_{0}}{a} = \frac{y - y_{0}}{b} = \frac{z - z_{0}}{c} = t$

Step 2

$F r o m t h e a b o v e e q u a t i o n, (a, b, c) = (0, - 1, 5) a n d (x_{0}, y_{0}, z_{0}) = (2, 0, - 3) S u b s t i t u t e a l l t h e v a l u e s a n d f i n d t h e e q u a t i o n .$

$\frac{x - 2}{0} = \frac{y - 0}{- 1} = \frac{z + 3}{5} = t A n d, x = 2, y = - t a n d z = - 3 + 5 t T h e p a r a m e t r i c e q u a t i o n i s r (t) = (2, - t, - 3 + 5 t) .$

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

Knowledge Booster

$Cartesian Coordinates$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,