Ignoring direction (negative signs)

❌ The Mistake in Action

In a triangle $OAB$, $\vec{OA} = \mathbf{a}$ and $\vec{OB} = \mathbf{b}$. Find $\vec{AB}$.

Wrong: $\vec{AB} = \mathbf{a} + \mathbf{b}$

🧠 Why It Happens

Students look at the letters $\mathbf{a}$ and $\mathbf{b}$ and just add them, ignoring the arrows on the diagram. They forget that to go from A to B, they must go against the arrow for $\mathbf{a}$.

✅ The Fix

To go from A to B via O:

Start at A, go to O: This is against the arrow, so $-\mathbf{a}$.
Go from O to B: This is with the arrow, so $+\mathbf{b}$.

$$\vec{AB} = -\mathbf{a} + \mathbf{b} = \mathbf{b} - \mathbf{a}$$

🔍 Spot the Mistake

Can you identify where this student went wrong?

Find vector AB given OA=a and OB=b

Path is A to O to B

AB = a + b

= b - a

Click on the line that contains the error.

📚 Related Topics

Learn more about the underlying maths: