   Chapter 11.5, Problem 22E

Chapter
Section
Textbook Problem

# Using Parametric and Symmetric EquationsIn Exercises 25–28, find the coordinates of a point P on the line and a vector v parallel to the line. x = 4 t , y = 5 − t , z = 4 + 3 t

To determine

To calculate: Find the coordinates of a point P on the line and the vector v parallel to the line.

Explanation

Given:

The equations of the lineare:

x=4t,y=5t and z=4+3t

Formula used:

The parametric equations of a line are:

x=x1+at,y=y1+bt and z=z1+ct

Calculation:

Coefficients of the parameter t, that is a,b, and c are the parallel direction numbers to that line.

As we know formula for parametric equations of a line, x1,y1 and z1 are the coordinates of the point through which line is passing.

The provided equation for the line is

x=4t,y=5t and z=4+3t

Now, the standard parametric equations of the lineare:

x=x1+at,y=y1+bt and z=z1+

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