Vector Addition, Subtraction, and Resultants
For vectors A and B separated by angle theta, the resultant is R = A + B and its squared magnitude follows the cosine rule; A - B is obtained by reversing B.
Why this shows up in the exam
Combining concurrent forces · Adding successive displacements · Finding relative separations and polygon resultants
Learn the idea
Vector sums depend on both magnitudes and the angle between directions. Joining arrows head to tail shows why aligned vectors reinforce, opposite vectors cancel, and oblique vectors produce a diagonal resultant. Subtraction means adding the reversed arrow.
🧠 Memory hook: Add arrows head to tail; subtract by turning the second arrow around.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- |A+B|² = A² + B² + 2AB cos(theta) — magnitude of a two-vector sum
- |A-B|² = A² + B² - 2AB cos(theta) — magnitude of a vector difference
- R_vector = sum A_i_vector — component-wise superposition of any number of vectors
How to approach it
- 1Translate the wording into a vector equation
- 2Choose components or the cosine rule
- 3Check limiting cases theta = 0 and theta = 180 degrees
Common slip-ups that cost marks
- •Adding magnitudes regardless of direction
- •Using the sum formula for a difference
- •Solving only for magnitude when direction is asked
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A particle has initial speed 2 m/s and constant acceleration 3 m/s^2 for 4 s. What distance does it cover?
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