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UPMSP Intermediate Physics - Code 151 study materials
UPMSP Intermediate Physics - Code 151 study resources

UPMSP Intermediate Physics - Code 151: Vectors and Measurement

UPMSP Intermediate Physics - Code 151 · Work through your exam, one topic at a time.

All guide sections

Vectors and Measurement

This unit supplies the language of the rest of the paper: scalars versus vectors, addition and resolution, dot and cross products, relative velocity, SI units, dimensions, significant figures and error propagation. It is rarely asked as a big derivation, but it appears inside almost every other numerical, and one or two 1-mark items on dimensional formulas or percentage error are almost guaranteed.

Core rules

  • Addition: triangle or parallelogram law; for two vectors, R = √(A² + B² + 2AB cosθ), with tan α = B sinθ/(A + B cosθ).
  • Resolution: Aₓ = A cosθ, A_y = A sinθ; resultants are found by adding components and recombining.
  • Dot product A·B = AB cosθ, a scalar; it vanishes for perpendicular vectors. Cross product |A×B| = AB sinθ, a vector perpendicular to both by the right-hand rule; its magnitude equals the area of the parallelogram.
  • Unit vectors: A = Aₓî + A_yĵ + A_z k̂, with |A| = √(Aₓ² + A_y² + A_z²).
  • Dimensions: homogeneity of an equation means every term has the same dimensions; dimensionless quantities include strain, refractive index and relative density.
  • Errors: for sums and differences, absolute errors add; for products and quotients, relative (percentage) errors add; raising to a power n multiplies the percentage error by n.

Worked example

Given A = 3î + 4ĵ and B = 4î − 3ĵ, find |A|, the dot product and the magnitude of the cross product. |A| = √(9 + 16) = 5; |B| = 5. A·B = (3)(4) + (4)(−3) = 12 − 12 = 0, so A and B are perpendicular. A×B = (3)(−3) − (4)(4) = −25 in the k̂ direction, so the magnitude is 25 square units - the area of the parallelogram they span, which also equals 5 × 5 × sin 90°.

Traps that cost marks

  • Writing the magnitude of a cross product as a scalar when it should be quoted with direction (or vice versa for the dot product).
  • Adding absolute errors in a product instead of adding relative errors.
  • Forgetting that sin θ, not cos θ, appears in the cross product and in the magnetic force.
  • Retaining more significant figures in the answer than in the least precise data.