tangent planes and normal lines
DESCRIPTION
Tangent Planes and Normal Lines. Finding a unit normal vector to the surface at the given point. 1. Find a unit normal vector to the surface at the given point. (Similar to p.951 #5-16). 2. Find a unit normal vector to the surface at the given point. (Similar to p.951 #5-16). - PowerPoint PPT PresentationTRANSCRIPT
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Tangent Planes and Normal Lines
![Page 2: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/2.jpg)
Finding a unit normal vector to the surface at the given point.
![Page 3: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/3.jpg)
1. Find a unit normal vector to the surface at the given point.
(Similar to p.951 #5-16)
)0,5,2(,0325 zyx
![Page 4: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/4.jpg)
2. Find a unit normal vector to the surface at the given point.
(Similar to p.951 #5-16)
)2,1,3(,3 2 yxz
![Page 5: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/5.jpg)
Finding an equation of the tangent plane to the surface at the given point
(xo, yo, zo)
![Page 6: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/6.jpg)
3. Find an equation of the tangent plane to the surface at the given point(Similar to p.951 #17-30)
)7,1,3(,3),( 22 yyxyxf
![Page 7: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/7.jpg)
4. Find an equation of the tangent plane to the surface at the given point(Similar to p.951 #17-30)
)1,3,2(,),( 23 yxeyxf
![Page 8: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/8.jpg)
5. Find an equation of the tangent plane to the surface at the given point(Similar to p.951 #17-30)
)3,8,1(),5(24 zxy
![Page 9: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/9.jpg)
Finding an equation of the tangent plane to the surface at the given point
and symmetric equations
![Page 10: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/10.jpg)
6. Find an equation of the tangent plane and find symmetric equations of the normal line to the
surface at the given point.(Similar to p.951 #31-40)
)1,2,1(,072 222 zyx
![Page 11: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/11.jpg)
7. Find an equation of the tangent plane and find symmetric equations of the normal line to the
surface at the given point.(Similar to p.951 #31-40)
)0,2,0(,2xyez
![Page 12: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/12.jpg)
Finding angle of inclination θ of the tangent plane to the surface at the
given point
![Page 13: Tangent Planes and Normal Lines](https://reader030.vdocument.in/reader030/viewer/2022012315/5681367d550346895d9e0956/html5/thumbnails/13.jpg)
8. Find the angle of inclination θ of the tangent plane to the surface at the given point.
(Similar to p.951 #47-50)
)2,1,3(,0522 zyx