   Chapter 11.5, Problem 13E

Chapter
Section
Textbook Problem

# Finding Parametric EquationsIn Exercises 17–24, find a set of parametric equations of the line with the given characteristics.The line passes through the point ( 2 , 3 , 4 ) and is parallel to the xz-plane and the yz-plane.

To determine

To calculate: Find Set of parametric equations of a line passing through the

point (2,3,4) and is parallel to the xz-plane and yz-plane

Explanation

Given:

The line passes through the point (2,3,4) and

is parallel to the xz-plane and yz-plane.

Formula used:

The parametric equations of a line are:

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

Cross product of two vectors:

n1×n2=|ijka1a2a3b1b2b3|

Calculation:

Cross product of two vector quantities results in a mutually perpendicular third quantity.

Therefore, the cross product of the normal vectors of both the planes will be a parallel vector to the line.

Then normal vector of xz-plane will be in y direction.

As we know the given line is parallel to both xz-plane and yz-plane,

Implies, that the line is perpendicular to the normal vector of both the planes.

n1=0,1,0.

Further the normal vector of yz-plane will be in x direction.

then,

n2=1,0,0.

Further let us find the cross product of two vectors:

n1×n2=|ijka1a2a3b1b2b3|

Again substituting the values

And only then find cross product of two vectors,

n1×n2=|ijk010100|=|100

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