Full unit practice requiring complete reasoning and representation checks.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u09-l01', 'number': 1, 'title': 'Vectors: Magnitude, Direction & Notation', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Find the magnitude of ⟨3,4⟩.
2. {'id': 'u09-l01', 'number': 1, 'title': 'Vectors: Magnitude, Direction & Notation', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Write a vector of magnitude 10 at 30° in component form.
3. {'id': 'u09-l01', 'number': 1, 'title': 'Vectors: Magnitude, Direction & Notation', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Add ⟨2,−1⟩ and ⟨5,4⟩.
4. {'id': 'u09-l01', 'number': 1, 'title': 'Vectors: Magnitude, Direction & Notation', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Compute ⟨1,2⟩·⟨3,−4⟩.
5. {'id': 'u09-l01', 'number': 1, 'title': 'Vectors: Magnitude, Direction & Notation', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Are ⟨2,1⟩ and ⟨1,−2⟩ orthogonal?
6. {'id': 'u09-l01', 'number': 1, 'title': 'Vectors: Magnitude, Direction & Notation', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Find the unit vector in the direction of ⟨6,8⟩.
7. {'id': 'u09-l02', 'number': 2, 'title': 'Vector Components and Resultants', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Find the magnitude of ⟨3,4⟩.
8. {'id': 'u09-l02', 'number': 2, 'title': 'Vector Components and Resultants', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Write a vector of magnitude 10 at 30° in component form.
9. {'id': 'u09-l02', 'number': 2, 'title': 'Vector Components and Resultants', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Add ⟨2,−1⟩ and ⟨5,4⟩.
10. {'id': 'u09-l02', 'number': 2, 'title': 'Vector Components and Resultants', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Compute ⟨1,2⟩·⟨3,−4⟩.
11. {'id': 'u09-l02', 'number': 2, 'title': 'Vector Components and Resultants', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Are ⟨2,1⟩ and ⟨1,−2⟩ orthogonal?
12. {'id': 'u09-l02', 'number': 2, 'title': 'Vector Components and Resultants', 'family': 'vectors', 'week': 26, 'unit': 9, 'unit_title': 'Vectors, Parametric Equations & Motion', 'essential': 'How do vectors and parameters represent magnitude, direction, components, paths, velocity, and two-dimensional motion?', 'project': 'Vector Navigation & Parametric Motion Lab'}
Find the unit vector in the direction of ⟨6,8⟩.