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Chapter 10: Q .38. (page 849)

In Exercises 35鈥�38, find an equation of the line of intersection of the two given planes.

x-2z=7andx-3y-4z=0

Short Answer

Expert verified

The equation isr(t)=鉄�2-3t,-3+3t,5+2t鉄�.

Step by step solution

01

Step 1:Given information

Consider the pcintsP(2,-3,5),Q(3,1,0)andR(-1,0,7)

02

Step 2:Calculation

Consider the pointsP(2,-3,5),Q(3,1,0)andR(-1,0,7).

The equation of the line containing the pointsAx0,y0,z0andBx1,y1,z1is given by:

r(t)=x0+at,y0+bt,z0+ct

Where, 鉄�a,b,c鉄�=x1-x0,y1-y0,z1-z0

The equation of line containing the pointsP(2,-3,5)andR(-1,0,7)is:

r(t)=鉄�2+t(-1-2),-3+t(0+3),5+t(7-5)鉄�

=鉄�2-3t,-3+3t,5+2t鉄�

Therefore, the equation of line the pointsP(2,-3,5)andR(-1,0,7)is

r(t)=鉄�2-3t,-3+3t,5+2t鉄�.

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