The displacement vector has scalar components of Ax = 80.0 m and Ay = 60.0 m. The displacement vector has a scalar component of Bx = 60.0 m and a magnitude of B = 75.0 m. The displacement vector has a magnitude of C = 100.0 m and is directed at an angle of 36.9° above the +x axis. Determine which two of these vectors are equal.
A and C. Pythagorean theorem
To determine which two vectors are equal, we need to compare their magnitudes and directions. Let's go through each pair of vectors and compare them:
1. Vector A and Vector B:
- Magnitude of Vector A: |A| = √(Ax² + Ay²) = √(80.0² + 60.0²) = √(6400 + 3600) = √10000 = 100.0 m
- Magnitude of Vector B: |B| = 75.0 m
- The magnitudes of Vector A and Vector B are not equal, so they are not equal.
2. Vector A and Vector C:
- Magnitude of Vector C: |C| = 100.0 m
- The magnitudes of Vector A and Vector C are equal, but we also need to compare their directions.
- The direction of Vector C is given as an angle of 36.9° above the +x axis.
- Since no direction is given for Vector A, we cannot compare their directions.
- Therefore, we cannot determine whether Vector A and Vector C are equal.
3. Vector B and Vector C:
- Magnitude of Vector C: |C| = 100.0 m
- Magnitude of Vector B: |B| = 75.0 m
- The magnitudes of Vector B and Vector C are not equal, so they are not equal.
In conclusion, none of the given vectors are equal to each other.
To determine which two vectors are equal, we can compare their magnitudes and components. Let's analyze each displacement vector:
Displacement vector A:
- Scalar components: Ax = 80.0 m, Ay = 60.0 m.
Displacement vector B:
- Scalar components: Bx = 60.0 m.
- Magnitude: B = 75.0 m.
Displacement vector C:
- Magnitude: C = 100.0 m.
- Direction: 36.9° above the +x axis.
To check if two vectors are equal, we need to compare their magnitudes and components.
Comparing vectors A and B:
- Magnitude of A = √(Ax² + Ay²) = √(80.0² + 60.0²) ≈ 100.0 m.
- Magnitude of B = 75.0 m.
- Therefore, vector A and vector B are NOT equal since their magnitudes differ.
Comparing vectors A and C:
- Magnitude of A = √(Ax² + Ay²) = √(80.0² + 60.0²) ≈ 100.0 m.
- Magnitude of C = 100.0 m.
- Therefore, vector A and vector C ARE equal since their magnitudes are the same.
Thus, vector A and vector C are equal.