Ever wondered why '5 km' is not enough to find a place?
Obi's okada rider asks, 'Five kilometres — but which way?' Knowing only the distance isn't enough; you also need the direction. A quantity with both size and direction is a vector.
Revision notes
Describe a movement by size AND direction with column vectors, and find a vector's length with Pythagoras.
Obi's okada rider asks, 'Five kilometres — but which way?' Knowing only the distance isn't enough; you also need the direction. A quantity with both size and direction is a vector.
A scalar has size only, like mass, time or a price in naira. A vector has size and direction, like displacement, velocity or force.
We write a vector as a column vector: 3−2 means 3 units right (across) and 2 units down.
Positive top number → right, negative → left. Positive bottom number → up, negative → down. Vectors are named in bold, like a, or by their end points, like AB.
🔑 Key idea: Top number = across, bottom number = up.
To go from A to B, subtract: AB = B − A (finish minus start).
For A(1, 2) and B(4, −2): AB = 4 − 1−2 − 2 = 3−4.
Going back the other way reverses both signs: BA = −34. The position vector of a point P(x, y) is the vector from the origin O to P.
🔑 Key idea: AB = B − A, and BA = −AB.
The magnitude |a| is the length of the arrow. The components form a right-angled triangle, so use Pythagoras.
|3−4| = √(32 + (−4)2) = √(9 + 16) = √25 = 5.
Squaring removes the minus sign, so a magnitude is never negative.
🔑 Key idea: |xy| = √(x2 + y2)
A is the point (−6, −6) and B is (−6, 4). Find the vector AB.
Step 1: Finish minus start
AB = −6 − (−6)4 − (−6)
= 010
Why? The vector tells you how far to move across and up to get from A to B.
Answer: 010
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.