๐ Scalar and Vector: Summary Note for MCQ
๐น 1. Scalar Quantities
Have only magnitude, no direction.
Can be added algebraically.
Examples:
Distance
Speed
Mass
Time
Temperature
Energy
๐น 2. Vector Quantities
Have both magnitude and direction.
Represented by arrows (โ).
Need vector rules for addition and subtraction.
Examples:
Displacement
Velocity
Acceleration
Force
Momentum
๐น 3. Representation of a Vector
Shown by an arrow pointing in the direction of the vector.
Length of arrow โ Magnitude.
Written as: โA or ๐ดโ
Unit vector: Aฬ = A/|A|, direction only.
๐น 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.
๐น 5. Vector Resolution
A vector A can be resolved into:
Ax = A cosฮธ (horizontal component)
Ay = A sinฮธ (vertical component)
๐น 6. Resultant of Two Vectors (Angle ฮธ Between Them)
R=A2+B2+2ABcosโกฮธR = sqrt{A^2 + B^2 + 2ABcostheta}
๐น 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
๐น 8. Scalar (Dot) Product
A ยท B = AB cosฮธ
The result is a scalar
Used in: Work, Power
๐น 9. Vector (Cross) Product
A ร B = AB sinฮธ nฬ
The result is a vector
Used in: Torque, Angular momentum
Direction from the Right-Hand Rule
โ 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