Motion in a Plane

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Scalar quantity: Has only magnitude, no direction. Examples: distance, mass, temperature, time. Vector quantity: Has both magnitude and direction, follows vector algebra rules. Examples: displacement,

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Vector representation: • Bold face: v (in print) • Arrow notation: v̅ (handwritten) • Magnitude notation: |v| = v Example: Position vector r with magnitude |r| = r The magnitude is always positive an

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Displacement vector: The straight line from initial position to final position, independent of the actual path taken. Key differences: • Displacement depends only on start and end points • Distance d

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Two vectors A and B are equal if and only if: 1. Same magnitude: |A| = |B| 2. Same direction Yes, vectors at different positions can be equal if they have the same magnitude and direction. Vector equ

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When multiplying vector A by scalar λ: If λ > 0: λA has magnitude λ|A| and same direction as A If λ < 0: λA has magnitude |λ||A| and opposite direction to A If λ = 0: λA = 0 (null vector) Examples:

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Triangle Law of Vector Addition: 1. Place tail of vector B at head of vector A 2. Join tail of A to head of B to get resultant R = A + B Commutative Property: A + B = B + A This means vector addition

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Null Vector (0): A vector with zero magnitude. Its direction is undefined. Main Properties: 1. A + 0 = A (adding null vector doesn't change original vector) 2. λ0 = 0 (scalar multiple of null vector

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Unit Vectors: Vectors with magnitude = 1, used to specify direction only. • î: unit vector along x-axis • ĵ: unit vector along y-axis • k̂: unit vector along z-axis • |î| = |ĵ| = |k̂| = 1 General