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Chapter 11: Q.53 (page 872)

Find all points of intersection between the vector function

r(t)=t,t2,t3and the plane defined by 3x鈭�3y+z=1.

Short Answer

Expert verified

3x-3y+z=1

1,1,1,1,1,1and1,1,1

Step by step solution

01

Given Information

The objective of this problem is to find all point of intersection between the vector function and the plane.

Vector function

rt=t,t2,t3Theplaneis3x-3y+z=1

02

Calculation

Substitute x=t,y=t2andz=t3in the equation of plane

3t-3t2+t3=1t3-1-3t2+3t=0t-1t2+t+1-3tt-1=0t-1t2-2t+1=0t-13=0t=1,1,1

Thus the points of intersection are

localid="1650021665961" 1,1,1,1,1,1and1,1,1

This shows that the vector function passes through the plane at a single point three times.

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