πŸ“˜ Scalar and Vector

πŸ“˜ Scalar and Vector: Summary Note for MCQ

Scalar and Vector

πŸ”Ή 1. Scalar Quantities

  • Have only magnitude, no direction.

  • Can be added algebraically.

  • Examples:

    • Distance

    • Speed

    • Mass

    • Time

    • Temperature

    • Energy

πŸ”Ή 2. Vector Quantities

  • Have both magnitude and direction.

  • Represented by arrows (β†’).

  • Need vector rules for addition and subtraction.

  • Examples:

    • Displacement

    • Velocity

    • Acceleration

    • Force

    • Momentum

πŸ”Ή 3. Representation of a Vector

  • Shown by an arrow pointing in the direction of the vector.

  • Length of arrow ∝ Magnitude.

  • Written as: β†’A or 𝐴⃗

  • Unit vector: AΜ‚ = A/|A|, direction only.

πŸ”Ή 4. Vector Addition (Triangle & Parallelogram Law)

  • Triangle Law: Place the tail of the second vector on the head of the first; the result is from the tail of the first to the head of the second.

  • Parallelogram Law: Two vectors from the same point; resultant is diagonal.

πŸ”Ή 5. Vector Resolution

  • A vector A can be resolved into:

    • Ax = A cosΞΈ (horizontal component)

    • Ay = A sinΞΈ (vertical component)

πŸ”Ή 6. Resultant of Two Vectors (Angle ΞΈ Between Them)

R=A2+B2+2ABcos⁑θR = sqrt{A^2 + B^2 + 2ABcostheta}

πŸ”Ή 7. Types of Vectors

  • Null Vector: Zero magnitude

  • Unit Vector: Magnitude = 1

  • Equal Vectors: Same magnitude and direction

  • Opposite Vectors: Same magnitude, opposite direction

  • Collinear Vectors: Parallel (same or opposite direction)

  • Coplanar Vectors: Lie in the same plane

πŸ”Ή 8. Scalar (Dot) Product

  • A Β· B = AB cosΞΈ

  • The result is a scalar

  • Used in: Work, Power

πŸ”Ή 9. Vector (Cross) Product

  • A Γ— B = AB sinΞΈ nΜ‚

  • The result is a vector

  • Used in: Torque, Angular momentum

  • Direction from the Right-Hand Rule

❗ Important MCQ Tips

  • Displacement is a vector; distance is a scalar

  • Work is scalar, even though it involves vectors

  • Vectors cannot be added like numbers unless the directions are the same

  • Use Pythagoras when vectors are perpendicular

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