Answers to Math Exercises & Math Problems: Relative Position, Distance and Deviation Between Points, Lines and Planes

 

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1.

 

Relative position, distance and deviation between points, lines and planes - Answers to Exercise 1

 

2.

 

Relative position, distance and deviation between points, lines and planes - Answers to Exercise 2

 

3.

 

Relative position, distance and deviation between points, lines and planes - Answers to Exercise 3

 

4.

 

Relative position, distance and deviation between points, lines and planes - Answers to Exercise 4

 

5.

 

Relative position, distance and deviation between points, lines and planes - Answers to Exercise 5

 

6.

 

Relative position, distance and deviation between points, lines and planes - Answers to Exercise 6

 

7.

 

Relative position, distance and deviation between points, lines and planes - Answers to Exercise 7

 

8. d = 6.5

 

9. d = sqrt(3)/3 = 0.58

 

10. d = sqrt(14)/21 = 0.18

 

11. p: x + y – 12 = 0

 

12. p1: x – 3 = 0; p2: x – y × sqrt(3) – 3 = 0

 

13. p1: y – 3 = 0; p2: 4x + 3y – 17 = 0

 

14. A' [ 3 ; –4 ; 8 ]

 

15. A [ –2 ; 5 ]; B [ 1 ; –3 ]; C [ 5 ; –9 ]; D [ 8 ; –17 ]

 

16. α = 104°; β = γ = 38°

 

17. C [ 6 ; –6 ]

 

18. A [ –4 ; –3 ]; B [ –5 ; 4 ]; C [ 3 ; –2 ]

 

19. α = 87°35'; β = 25°45'

 

20. a) d = 5 × sqrt(2) = 7.07
b) d = sqrt(246)/2 = 7.84
c) d = sqrt(221)/2 = 7.43
d) d = (5/2) × sqrt(2) = 3.54
 e) φ = 88°55'
f) φ = 39°18'
g) φ = 71°24'
h) φ = 53°36'
i) φ = 63°12'
j) φ = 36°54'

 

 

 

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