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If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position P2=[X2,Y2,Z3]

If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position P2=[X2,Y2,Z3]

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position P2=[X2,Y2,Z3]

Expert Solution
Step 1

Solution ) suppose P1 [ x1 y1 , z1] is rotated about z axis so new point P2 [ x2 , y2 , z2 ] is given by 

x2 = x1cos θ  - y1 sin θ

y2 = x1cos θ  +  y1 sin θ

z2 = z1 

[ x1 y1 , z1 ] = [10,10,10]

x2 = 10 cos 60  - 10 sin 60 

x2 = 10(1/2) - 10 × (√3/2 )

x2 = 5 - 5√3 

y2 = 10 cos60 + 10 sin 60

y2 = 10(1/2) + 10 × (√3/2 )

y2 = 5 + 5 √3

z2 = 10

Hence point will be 

P2 = [ 5 -  5 √3 , 5 + 5 √3 , 10 ]

 

 

 

 

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