Problem 2 For the 3d object shown to the right, complete the following: a) Determine the position vector from A to B in Cartesian notation. b) Determine the position vector from A to C in Cartesian notation. c) Determine the angle (0) between line segments AB and AC. d) Determine the unit vector in the direction of line segment AC. e) Determine how much (i.e. what length) of line segment AB is parallel 1 m z I m' 5 m -3 m- B 4 m 3 m y

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem 2**

For the 3D object shown to the right, complete the following:

a) Determine the position vector from A to B in Cartesian notation.

b) Determine the position vector from A to C in Cartesian notation.

c) Determine the angle (θ) between line segments AB and AC.

d) Determine the unit vector in the direction of line segment AC.

e) Determine how much (i.e., what length) of line segment AB is parallel to line segment AC.

**Diagram Explanation:**

The diagram shows a 3D object positioned within a rectangular coordinate system with axes labeled x, y, and z. 

- Point A is located at coordinates (1, 1, 0).
- Point B is located directly above Point A at coordinates (1, 4, 3).
- Point C is located on the x-y plane at coordinates (5, 3, 0).
- The line segments AB and AC form a triangular face, with θ representing the angle between these segments.

Distances in the diagram:
- From the origin (0,0,0) to A is 1 meter along both x and y axes.
- From A to B is 3 meters along the z-axis.
- From A to C: 5 meters along the x-axis and 2 meters along the y-axis.
Transcribed Image Text:**Problem 2** For the 3D object shown to the right, complete the following: a) Determine the position vector from A to B in Cartesian notation. b) Determine the position vector from A to C in Cartesian notation. c) Determine the angle (θ) between line segments AB and AC. d) Determine the unit vector in the direction of line segment AC. e) Determine how much (i.e., what length) of line segment AB is parallel to line segment AC. **Diagram Explanation:** The diagram shows a 3D object positioned within a rectangular coordinate system with axes labeled x, y, and z. - Point A is located at coordinates (1, 1, 0). - Point B is located directly above Point A at coordinates (1, 4, 3). - Point C is located on the x-y plane at coordinates (5, 3, 0). - The line segments AB and AC form a triangular face, with θ representing the angle between these segments. Distances in the diagram: - From the origin (0,0,0) to A is 1 meter along both x and y axes. - From A to B is 3 meters along the z-axis. - From A to C: 5 meters along the x-axis and 2 meters along the y-axis.
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