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Chapter 10: Q 22. (page 845)

Find the equations of the planes determined by the given conditions.

The plane contains the point (鈭�2,3,鈭�1)and is normal to the vector 3i鈭�2j

Short Answer

Expert verified

The equation of the plane that is determined by the given conditions is 3x-2y+12=0

Step by step solution

01

Given information

The plane that contains the point (-2,3,-1) and is normal to the vector 3i-2j

02

Calculation

The goal is to determine the plane equation that is determined by the given conditions.

The equation of the plane with r0 a point that lies in the plane and n a vector normal to the plane is given by:

n路r-r0=0

The normal vector is:

n=鉄�3,-2,0鉄�

The point r0is:

r0=(-2,3,-1)
03

Calculation

The equation of the plane that contains the point (-2,3,-1) and is normal to the vector 3i-2j is:

鉄�3,-2,0鉄�路(鉄�x,y,z鉄�-(-2,3,-1))=0(Substitution)3x-2y-(3(-2)-2(3)+0(-1))=0(Simplify)3x-2y-(-6-6+0)=03x-2y+12=0

Thus, the equation of the plane that is determined by the given conditions is 3x-2y+12=0

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Most popular questions from this chapter

Find vand find the unit vector in the direction of v.

v=3,鈭�4

Find the norm of the vector.v=0,0,6

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u=1,2,v=3,5

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Use limit rules and the continuity of power functions to prove that every polynomial function is continuous everywhere.
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