
π Scalar and Vector: Summary Note for MCQ
πΉ 1. Scalar Quantities
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Have only magnitude, no direction.
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Can be added algebraically.
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Examples:
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Distance
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Speed
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Mass
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Time
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Temperature
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Energy
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πΉ 2. Vector Quantities
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Have both magnitude and direction.
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Represented by arrows (β).
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Need vector rules for addition and subtraction.
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Examples:
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Displacement
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Velocity
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Acceleration
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Force
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Momentum
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πΉ 3. Representation of a Vector
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Shown by an arrow pointing in the direction of the vector.
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Length of arrow β Magnitude.
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Written as: βA or π΄β
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Unit vector: AΜ = A/|A|, direction only.
πΉ 4. Vector Addition (Triangle & Parallelogram Law)
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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.
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Parallelogram Law: Two vectors from the same point; resultant is diagonal.
πΉ 5. Vector Resolution
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A vector A can be resolved into:
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Ax = A cosΞΈ (horizontal component)
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Ay = A sinΞΈ (vertical component)
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πΉ 6. Resultant of Two Vectors (Angle ΞΈ Between Them)
R=A2+B2+2ABcosβ‘ΞΈR = sqrt{A^2 + B^2 + 2ABcostheta}
πΉ 7. Types of Vectors
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Null Vector: Zero magnitude
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Unit Vector: Magnitude = 1
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Equal Vectors: Same magnitude and direction
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Opposite Vectors: Same magnitude, opposite direction
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Collinear Vectors: Parallel (same or opposite direction)
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Coplanar Vectors: Lie in the same plane
πΉ 8. Scalar (Dot) Product
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A Β· B = AB cosΞΈ
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The result is a scalar
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Used in: Work, Power
πΉ 9. Vector (Cross) Product
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A Γ B = AB sinΞΈ nΜ
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The result is a vector
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Used in: Torque, Angular momentum
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Direction from the Right-Hand Rule
β Important MCQ Tips
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Displacement is a vector; distance is a scalar
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Work is scalar, even though it involves vectors
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Vectors cannot be added like numbers unless the directions are the same
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Use Pythagoras when vectors are perpendicular