Problem: 5 coordinates are given: A(-1, 4, 5), B(2, -1, -2), C(-6, -8, 3) in RCS; D(5, n, -12) in CCS; and E(8, t/3, 3n/2) in SCS. Let point O be the origin. Do the following: 1. Convert the following coordinates given below: a. Coordinate C to CCS: C → C(pc, pc, zc) b. Coordinate C to SCS: C → c. Coordinate D to RCS: D → D(XD, YD, ZD) d. Coordinate D to SCS: D → D(ro, Oo, po) e. Coordinate E to RCS: E → E(XE, YE, Ze) f. Coordinate E to CCS: E → E(pe, de, ze) ans: (10, –126.87,3) → ans: (10.440, 73.30, –126.87) - ans: (-5,0, 12) - ans: (13, 157.38, 180) → ans: (0, –6.928,4) → ans: (6.928, –90, 4) C(rc, Oc, ̟c) 2. Find the following vectors between two points: a. Vector directed from C to D. Label it as: RcD = Rxco + Ryco + Rzco in RCS → ans: < 1,8, –15 > b. Vector directed from D to E. Label it as: RDE = RPDE + RộDE + RZDE in CCS → ans: < -5, 6.928, 16 > c. Vector directed from E to C. Label it as: Rec = Rrec + Roec + Rec in SCs ans: < 0.428, 1.402, –6 >

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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Please send a solution for number 2 :) Thank you!

Note: Use the proper representation for a vector, component vector, unit vector, and scalar quantities in
your solution. In this sample, all final answers in red ink are the format to be encoded in BB.
Problem: 5 coordinates are given: A(-1, 4, 5), B(2, -1, -2), C(-6, -8, 3) in RCS; D(5, T, -12) in CCS; and E(8, 1/3,
3n/2) in SCS. Let point O be the origin. Do the following:
1. Convert the following coordinates given below:
a. Coordinate C to CCS: C→ C(pc, ộc, zc)
b. Coordinate C to SCS: C → C(rc, Oc, oc)
c. Coordinate D to RCS: D→ D(XD, YD, ZD)
d. Coordinate D to SCS: D → D(rd, OD, oo)
ans: (10, –126.87,3)
→ ans: (10.440, 73.30, – 126.87)
→ ans: (-5,0, 12)
— аns: (13, 157.38, 180)
→ ans: (0, –6.928,4)
— аns: (6.928, -90,4)
E(XE, YE, ZE)
f. Coordinate E to CCS: E → E(pe, DE, Ze)
e. Coordinate E to RCS: E →
2. Find the following vectors between two points:
a. Vector directed from C to D. Label it as: RcD = Rxco + Ryco + RzcD in RCS
→ ans: < 1,8, –15 >
b. Vector directed from D to E. Label it as: RDE = RPDE + RODE + RZDE in CCS
→ ans: < -5, 6.928, 16 >
c. Vector directed from E to C. Label it as: RĘc = Rrec + Roec + RPec in SCS
→ ans: < 0.428, 1.402, –6 >
3. Find the distance between the two points given below:
a. Cto D - ans: 17.029
b. D to E → ans: 18.138
с. E to C ans: 16.176
4. Find the following unit vectors:
→ ans: < 0.059,0.470,–0.881 >
→- ans: < -0.276,0.382,0.882 >
→ ans: < 0.069,0.227,–0.971 >
a. aco in RCS
b. aDe in CCS
c. aɛc in SCS
5. From the previous number, convert vector Rec SCS to CCS.
→ ans:< 1.072, –6, –1 >
→ ans: 60.50
6. The angle between segments AC and AB.
7. The vector projection of the vector directed from A to B, to vector directed from O to C.
→ ans: < -0.055, –0.073,0.028 >
→ ans:5.523
8. The area of the triangle defined by points A, B, and O.
9. The unit vector perpendicular to the plane in which the triangle in #8 is located.
→ ans: +< -0.272, 0.724, –0.634 >
10. The volume of a parallelepiped if coordinates A, B, C, and O are its corners. → ans: 67
11. If vector Rec is going to be transferred from point E to A, determine Rec as a function of its new
→ ans: < -0.507,0.957,6.081 >
components in SCS.
12. If the tail of vector Rec is at A as in #11, determine the coordinate of its head in RCS.
→ ans: (-7,2.928,4)
Transcribed Image Text:Note: Use the proper representation for a vector, component vector, unit vector, and scalar quantities in your solution. In this sample, all final answers in red ink are the format to be encoded in BB. Problem: 5 coordinates are given: A(-1, 4, 5), B(2, -1, -2), C(-6, -8, 3) in RCS; D(5, T, -12) in CCS; and E(8, 1/3, 3n/2) in SCS. Let point O be the origin. Do the following: 1. Convert the following coordinates given below: a. Coordinate C to CCS: C→ C(pc, ộc, zc) b. Coordinate C to SCS: C → C(rc, Oc, oc) c. Coordinate D to RCS: D→ D(XD, YD, ZD) d. Coordinate D to SCS: D → D(rd, OD, oo) ans: (10, –126.87,3) → ans: (10.440, 73.30, – 126.87) → ans: (-5,0, 12) — аns: (13, 157.38, 180) → ans: (0, –6.928,4) — аns: (6.928, -90,4) E(XE, YE, ZE) f. Coordinate E to CCS: E → E(pe, DE, Ze) e. Coordinate E to RCS: E → 2. Find the following vectors between two points: a. Vector directed from C to D. Label it as: RcD = Rxco + Ryco + RzcD in RCS → ans: < 1,8, –15 > b. Vector directed from D to E. Label it as: RDE = RPDE + RODE + RZDE in CCS → ans: < -5, 6.928, 16 > c. Vector directed from E to C. Label it as: RĘc = Rrec + Roec + RPec in SCS → ans: < 0.428, 1.402, –6 > 3. Find the distance between the two points given below: a. Cto D - ans: 17.029 b. D to E → ans: 18.138 с. E to C ans: 16.176 4. Find the following unit vectors: → ans: < 0.059,0.470,–0.881 > →- ans: < -0.276,0.382,0.882 > → ans: < 0.069,0.227,–0.971 > a. aco in RCS b. aDe in CCS c. aɛc in SCS 5. From the previous number, convert vector Rec SCS to CCS. → ans:< 1.072, –6, –1 > → ans: 60.50 6. The angle between segments AC and AB. 7. The vector projection of the vector directed from A to B, to vector directed from O to C. → ans: < -0.055, –0.073,0.028 > → ans:5.523 8. The area of the triangle defined by points A, B, and O. 9. The unit vector perpendicular to the plane in which the triangle in #8 is located. → ans: +< -0.272, 0.724, –0.634 > 10. The volume of a parallelepiped if coordinates A, B, C, and O are its corners. → ans: 67 11. If vector Rec is going to be transferred from point E to A, determine Rec as a function of its new → ans: < -0.507,0.957,6.081 > components in SCS. 12. If the tail of vector Rec is at A as in #11, determine the coordinate of its head in RCS. → ans: (-7,2.928,4)
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