The magnitude of a vector is its length. Use Pythagoras: |(4, −1)| = √(16 + 1) = √17 ≈ 4.1. Leave answers as simplified surds when asked for exact values.
Two vectors are parallel if one is a multiple of the other. (10, 8) is parallel to (5, 4), because it is 2 times it. To find an unknown k in ka + b = c, set up an equation for the top and the bottom parts and solve.
Worked example
a = (−3, 1), b = (−5, 1) and ka + b = (−14, 4). Find k.
- Top: −3k − 5 = −14, so −3k = −9.
- k = 3. Check bottom: 3 + 1 = 4.
Answer:k = 3
Key words
- magnitude
- the length of a vector
- parallel
- one vector is a multiple of the other
- resultant
- the vector you get by adding
Practise this
New questions every time.
Common Core-referenced: HSN-VM.A.3