L3: SCALAR AND VECTOR QUANTITIES

Scalar

A physical quantity that has magnitude but no direction.

Vector

A physical quantity that has both magnitude and direction.

Cartesian Coordinate Plane

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Cardinal Directions for Vectors

• North

• South

• East

• West

• Northeast

• Northwest

• Southeast

• Southwest

Two ways to represent vectors

• Arrow form

• Magnitude direction form

Arrow form

• The tail of the arrow serves as the starting point of the vector

• The body of the arrow represents the magnitude. The longer the arrow, the higher the magnitude is.

• The arrowhead represents the direction of the vector.

Magnitude direction form

• A = 900 km, 70° East of North

• 900 km = magnitude

• 70° East of North = direction

Vector Addition in 1D

• Parallel Vectors

• Antiparallel Vectors

Parallel Vectors

• These are vectors heading in the same direction.

• When two vectors A and B are parallel, the magnitude of their sum equal the sum of their magnitudes.

Antiparallel Vectors

• These are vectors heading in the opposite direction.

• When two vectors A and B are antiparallel, the magnitude of their sum equals the difference of their magnitudes.

Sign Conventions: Parallel Vectors

• East/North: (+)

• West/South: (-)

• In adding vectors in one dimension using graphical method, follow the head to tail rule.

• Scale is the ratio between the distance on paper and the real life magnitude of the vectors.

• In head to tail, the resultant is from the tail of the first vector up to the head of the last vector.