Flashcards · 7357 · Topic 11

J: Vectors flashcards

9 cards on Topic 11. Pick a subtopic or study them all.

Study mode needs JavaScript. Every card is listed below, so you can still cover the answers and test yourself.

All 9 cards

For a quick read-through or printing. Cover the right-hand side to test yourself.

Magnitude of xi + yj and of xi + yj + zk: √(x² + y²) and √(x² + y² + z²).
Unit vector in the direction of a: â = a/|a|.
Vector →AB and distance AB from position vectors a and b: →AB = b − a; AB = |b − a|. Midpoint (a + b)/2.
Position vector of the point dividing AB in the ratio m : n: a + (m/(m + n))(b − a).
When are two vectors parallel?: When one is a non-zero scalar multiple of the other: b = ka.
A vector has magnitude r at angle θ to i. Write it in components.: r cos θ i + r sin θ j.
Find |2i − j + 2k| and the angle it makes with the z-axis (k).: |a| = √(4 + 1 + 4) = 3. cos θ = (k-component)/|a| = 2/3, so θ = 48.2°.
Is the scalar product a.b needed for AQA A-level Mathematics 7357?: No. The specification lists it as Further Maths only. Find angles from components and magnitudes instead.
Scalar vs vector quantities in mechanics: Scalars have size only (distance, speed, mass, time). Vectors have size and direction (displacement, velocity, acceleration, force).