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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, 3T/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, þC, zC) b. Coordinate C to SCS: C → C(rC, OC, 0C) c. Coordinate D to RCS: D→ D(xD, yD, zD) d. Coordinate D to SCS: D D(rD, OD, ØD) e. Coordinate E to RCS: E → E(xE, yE, zE) f. Coordinate E to CCS: E → E(pE, þE, zE) 2. Find the following vectors between two points and find the distance between the two points: a. Vector directed from C to D. Label it as: RCD = RXCD + RYCD + RZCD in RCS b. Vector directed from D to E. Label it as: RDE = RPDE + RODE + RZDE in CCS c. Vector directed from E to C. Label it as: REC = RREC + ROEC + RØEC in SCS 3. Find the following unit vectors: a. aCD in RCS b. aDE in CCS C. aEC in SCS 4. Find the following: a. From the previous number, convert vector REC SCS to CCS b. The angle between segments AC and AB c. The vector projection of the vector directed from A to B, to vector directed from O to C d. The area of the triangle defined by points A, B, and O e. The unit vector perpendicular to the plane in which the triangle in (d.) is located f. The volume of a parallelepiped if coordinates A, B, C, and O are its corners. g. If vector REC is going to be transferred from point E to A, determine REC as a function of its new components in SCS. h. If the tail of vector REC is at A as in (g.), determine the coordinate of its head in RCS

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, 3T/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, þC, zC) b. Coordinate C to SCS: C → C(rC, OC, 0C) c. Coordinate D to RCS: D→ D(xD, yD, zD) d. Coordinate D to SCS: D D(rD, OD, ØD) e. Coordinate E to RCS: E → E(xE, yE, zE) f. Coordinate E to CCS: E → E(pE, þE, zE) 2. Find the following vectors between two points and find the distance between the two points: a. Vector directed from C to D. Label it as: RCD = RXCD + RYCD + RZCD in RCS b. Vector directed from D to E. Label it as: RDE = RPDE + RODE + RZDE in CCS c. Vector directed from E to C. Label it as: REC = RREC + ROEC + RØEC in SCS 3. Find the following unit vectors: a. aCD in RCS b. aDE in CCS C. aEC in SCS 4. Find the following: a. From the previous number, convert vector REC SCS to CCS b. The angle between segments AC and AB c. The vector projection of the vector directed from A to B, to vector directed from O to C d. The area of the triangle defined by points A, B, and O e. The unit vector perpendicular to the plane in which the triangle in (d.) is located f. The volume of a parallelepiped if coordinates A, B, C, and O are its corners. g. If vector REC is going to be transferred from point E to A, determine REC as a function of its new components in SCS. h. If the tail of vector REC is at A as in (g.), determine the coordinate of its head in RCS

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter81: Introduction To Computer Numerical Control (cnc)
Section: Chapter Questions
Problem 18A
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Pls help me answer #4 c-e. Thank you very much!

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, T/3, 3t/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, 0C, zC) b. Coordinate C to SCS: C→ C(rC, OC, C) c. Coordinate D to RCS: D → D(xD, yD, zD) d. Coordinate D to SCS: D → D(rD, 0D, ØD) e. Coordinate E to RCS: E → E(xE, yE, zE) f. Coordinate E to CCS: E → E(pE, þE, zE) 2. Find the following vectors between two points and find the distance between the two points: a. Vector directed from C to D. Label it as: RCD = R×CD + RYCD + RZCD in RCS b. Vector directed from D to E. Label it as: RDE = RPDE + RODE + RZDE in CCS c. Vector directed from E to C. Label it as: REC = RREC + ROEC + R¢EC in SCS 3. Find the following unit vectors: a. aCD in RCS b. aDE in CCS C. aEC in SCS 4. Find the following: a. From the previous number, convert vector REC SCS to CCS b. The angle between segments AC and AB c. The vector projection of the vector directed from A to B, to vector directed from O to C d. The area of the triangle defined by points A, B, and O e. The unit vector perpendicular to the plane in which the triangle in (d.) is located f. The volume of a parallelepiped if coordinates A, B, C, and O are its corners. g. If vector REC is going to be transferred from point E to A, determine REC as a function of its new components in SCS. h. If the tail of vector REC is at A as in (g.), determine the coordinate of its head in RCS
Transcribed Image Text: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, T/3, 3t/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, 0C, zC) b. Coordinate C to SCS: C→ C(rC, OC, C) c. Coordinate D to RCS: D → D(xD, yD, zD) d. Coordinate D to SCS: D → D(rD, 0D, ØD) e. Coordinate E to RCS: E → E(xE, yE, zE) f. Coordinate E to CCS: E → E(pE, þE, zE) 2. Find the following vectors between two points and find the distance between the two points: a. Vector directed from C to D. Label it as: RCD = R×CD + RYCD + RZCD in RCS b. Vector directed from D to E. Label it as: RDE = RPDE + RODE + RZDE in CCS c. Vector directed from E to C. Label it as: REC = RREC + ROEC + R¢EC in SCS 3. Find the following unit vectors: a. aCD in RCS b. aDE in CCS C. aEC in SCS 4. Find the following: a. From the previous number, convert vector REC SCS to CCS b. The angle between segments AC and AB c. The vector projection of the vector directed from A to B, to vector directed from O to C d. The area of the triangle defined by points A, B, and O e. The unit vector perpendicular to the plane in which the triangle in (d.) is located f. The volume of a parallelepiped if coordinates A, B, C, and O are its corners. g. If vector REC is going to be transferred from point E to A, determine REC as a function of its new components in SCS. h. If the tail of vector REC is at A as in (g.), determine the coordinate of its head in RCS
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