Mathematical Methods
Maharashtra Board · Class 11 · Physics
Quick revision notes for Mathematical Methods — Maharashtra Board Class 11 Physics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Scalar and Vector Quantities
- Scalars are physical quantities completely described by magnitude only (distance, speed, mass, temperature)
- Vectors require both magnitude and direction for complete description (displacement, velocity, acceleration, force)
- Scalars follow ordinary algebraic rules for addition/subtraction
Vector Addition and Subtraction
- Triangle Law: If two vectors form two sides of triangle in order, resultant is third side in opposite direction
- Parallelogram Law: Two vectors from same point form adjacent sides, diagonal gives resultant
- Vector addition is commutative: A⃗ + B⃗ = B⃗ + A⃗
Vector Resolution and Components
- Any vector can be resolved into rectangular components along coordinate axes
- Components are projections of vector along chosen directions
- Ax = A cosθ, Ay = A sinθ for vector A⃗ at angle θ with x-axis
Scalar Product (Dot Product)
- Dot product gives scalar quantity from two vectors
- A⃗·B⃗ = AB cosθ where θ is angle between vectors
- Geometrically represents projection of one vector on another
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