   Chapter 11.5, Problem 77E

Chapter
Section
Textbook Problem

# Intersection of Planes In Exercises 75 and 76, (a) find the angle between the two planes, and (b) find a set of parametric equations for the line of intersection of the planes. 2 x − 2 y + z = 12 ,   x − 1 2 = y + ( 3 / 2 ) − 1 = z + 1 2

To determine

To calculate: The points of intersection of plane, 2x2y+z=12, and line, x12=y+(3/2)1=z+12, and also determine whether the provided line lies in the provided plane or not.

Explanation

Given:

The equation of the plane is,

2x2y+z=12

And, the equation of line is,

x12=y+(3/2)1=z+12

Formula used:

The symmetric equation of a line is:xx1a=yy1b=zz1c

Calculation:

First, convert the provided symmetric equation of line into the parametric equation of the line by equating it to the parameter 't'.

So, the parametric equations of the line are,

x12=y+(3/2)1=z+12=t

The first parametric equation is,

x12=tx=t+12

The second parametric equation is,

y+(3/2)1=ty+32=ty=t32

The third parametric equation is,

z+12=tz+1=2tz=2t1

So, from above calculation the parametric equations are,

x=t+12,y=t32 and z=2t1

Now, substitute the obtained values of x, y and z in the provided equation of plane to obtain the value of the parameter t.

The equation of the plane is,

2x2y+z=12

Substitute x=t+12,y=t32 and z=2t1

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