Ever wondered where the ball ends up after two passes?
Emeka passes the ball to Musa, and Musa passes it on to Yusuf. The ball made two moves, but you can describe the whole trip as ONE vector straight from Emeka to Yusuf — the resultant.
Revision notes
Add, subtract and scale vectors, find the length of a resultant, and spot parallel vectors.
Emeka passes the ball to Musa, and Musa passes it on to Yusuf. The ball made two moves, but you can describe the whole trip as ONE vector straight from Emeka to Yusuf — the resultant.
Add vectors by adding their components: 21 + 3−4 = 5−3.
The answer is the resultant: the single move from the start of the first vector to the end of the second (nose to tail).
Subtracting is adding the opposite: a − b = a + (−b), so subtract the tops and subtract the bottoms.
🔑 Key idea: Add or subtract top with top, bottom with bottom.
3a multiplies both components by 3: if a = 21 then 3a = 63 — same direction, three times as long. A negative multiple points the opposite way.
For 2a − b with b = 3−4: 42 − 3−4 = 16.
Vectors are parallel if one is a multiple of the other: 6−9 = 3 × 2−3, so they are parallel.
🔑 Key idea: b is parallel to a when b = ka.
To find |a + b|, work out a + b first, then use Pythagoras on the answer.
In general |a + b| is NOT |a| + |b|: walking 3 km east then 4 km north leaves you 5 km from the start, not 7 km.
🔑 Key idea: Combine first, then find the magnitude.
a = 5−4 and b = −1−2. Find 3a − 3b.
Step 1: Scale each vector
3a = 15−12
−3b = 36
Step 2: Add the components
15 + 3−12 + 6 = 18−6
Answer: 18−6
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.