Vectors Notes Class 11 FBISE NBF: Complete solved chapter on vectors for Class 11 Physics FBISE new syllabus. Easy explanations, derivations, examples, MCQs, short questions, numericals, assignments from Hamdard Science Academy PDF.
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Scalars and Vectors
Scalars: Magnitude only (e.g., mass 5 kg, speed 60 km/h).
Vectors: Magnitude and direction (e.g., displacement 10 m east, force 5 N downward).
Vector Resolution – Rectangular Components
Resolve vector into perpendicular components:
A_x = A cos θ, A_y = A sin θ.
Vector: A = A_x î + A_y ĵ.
From components: Magnitude A = √(A_x² + A_y²), direction θ = tan⁻¹(A_y / A_x).
Products of Vectors
Dot Product (Scalar Product)
A · B = AB cos θ = A_x B_x + A_y B_y + A_z B_z.
Commutative, zero if perpendicular.
Examples: Work W = F · d.
Cross Product (Vector Product)
A × B = AB sin θ n̂ (right-hand rule).
Component: Determinant form.
Magnitude equals parallelogram area.
Examples: Torque τ = r × F.
Special Vectors
- Unit Vector: Magnitude 1, â = A / |A|.
- Null Vector: Magnitude 0.
- Position Vector: r = x î + y ĵ + z k̂.
Exercises Solved
MCQs, short questions, comprehensive, numericals, assignments fully solved in PDF.
Master vectors chapter notes FBISE with these NBF physics unit 2 solved notes.
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