   Chapter 11, Problem 46RE

Chapter
Section
Textbook Problem

# Finding Parametric Equations In Exercises 43-46, find a set parametric equations of the line.The line passes through the point ( 0 , 1 , 4 ) u = 〈 2 , − 5 , 1 〉   a n d   v = 〈 − 3 , 1 , 4 〉 .

To determine

To calculate: The set of parametric equations of a line which passes through the point (0,1,4) and is perpendicular to u=2,5,1 and v=3,1,4.

Explanation

Given:

The line is passing through the point P(0,1,4) and is perpendicular to u=2,5,1 and v=3,1,4.

Formula used:

Parametric equation of a line is given by,

x=x1+aty=y1+btz=z1+ct.

Calculation:

Since, the provided line is perpendicular to both u and v, so the cross product of u and v will give the required parallel vector a of the line.

Thus,

a=u×v=|ijk251314|=|5114|i|2134|j+|2<

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