Answer :
To determine the magnitude and direction angle of the resultant vector given the expression [tex]\(5r - 3s + 8t\)[/tex], consider the provided numerical results for potential vectors. Here are four options:
1. Magnitude: 10.8, Direction: [tex]\(56.3^\circ\)[/tex]
2. Magnitude: 18.4, Direction: [tex]\(119.4^\circ\)[/tex]
3. Magnitude: 41.0, Direction: [tex]\(77.3^\circ\)[/tex]
4. Magnitude: 97.6, Direction: [tex]\(24.2^\circ\)[/tex]
These are given as possible resultant vectors.
Since we don't have specific vector components or calculations displayed in the original question, we can present each option as it stands:
- Option 1 has a magnitude of 10.8 and a direction angle of [tex]\(56.3^\circ\)[/tex].
- Option 2 has a magnitude of 18.4 and a direction angle of [tex]\(119.4^\circ\)[/tex].
- Option 3 has a magnitude of 41.0 and a direction angle of [tex]\(77.3^\circ\)[/tex].
- Option 4 has a magnitude of 97.6 and a direction angle of [tex]\(24.2^\circ\)[/tex].
For this type of question, typically, you would be expected to determine which of these resultant vectors most closely represents the sum of the given vectors [tex]\(5r - 3s + 8t\)[/tex] based on additional data on vectors [tex]\(r\)[/tex], [tex]\(s\)[/tex], and [tex]\(t\)[/tex] or based on detailed vector addition calculations.
Since the task doesn't explicitly detail the computational steps involved or specific data about vectors [tex]\(r\)[/tex], [tex]\(s\)[/tex], and [tex]\(t\)[/tex], these results are accepted as potential resultant vectors for consideration.
1. Magnitude: 10.8, Direction: [tex]\(56.3^\circ\)[/tex]
2. Magnitude: 18.4, Direction: [tex]\(119.4^\circ\)[/tex]
3. Magnitude: 41.0, Direction: [tex]\(77.3^\circ\)[/tex]
4. Magnitude: 97.6, Direction: [tex]\(24.2^\circ\)[/tex]
These are given as possible resultant vectors.
Since we don't have specific vector components or calculations displayed in the original question, we can present each option as it stands:
- Option 1 has a magnitude of 10.8 and a direction angle of [tex]\(56.3^\circ\)[/tex].
- Option 2 has a magnitude of 18.4 and a direction angle of [tex]\(119.4^\circ\)[/tex].
- Option 3 has a magnitude of 41.0 and a direction angle of [tex]\(77.3^\circ\)[/tex].
- Option 4 has a magnitude of 97.6 and a direction angle of [tex]\(24.2^\circ\)[/tex].
For this type of question, typically, you would be expected to determine which of these resultant vectors most closely represents the sum of the given vectors [tex]\(5r - 3s + 8t\)[/tex] based on additional data on vectors [tex]\(r\)[/tex], [tex]\(s\)[/tex], and [tex]\(t\)[/tex] or based on detailed vector addition calculations.
Since the task doesn't explicitly detail the computational steps involved or specific data about vectors [tex]\(r\)[/tex], [tex]\(s\)[/tex], and [tex]\(t\)[/tex], these results are accepted as potential resultant vectors for consideration.
