2D Vector Subtraction: Level 1 Example with Fractions
Given vectors \( u = \left\langle \frac{3}{4}, \frac{5}{6} \right\rangle \), \( v = \left\langle \frac{1}{2}, \frac{1}{3} \right\rangle \)
1. Write down vectors u and v: \( u = \left\langle \frac{3}{4}, \frac{5}{6} \right\rangle \), \( v = \left\langle \frac{1}{2}, \frac{1}{3} \right\rangle \)
2. Write down the negative of vector v: \( -v = \left\langle -\frac{1}{2}, -\frac{1}{3} \right\rangle \)
3. Add vector u and the negative of vector v: \( u – v = \left\langle \frac{3}{4}, \frac{5}{6} \right\rangle + \left\langle -\frac{1}{2}, -\frac{1}{3} \right\rangle \)
4. Perform the addition component-wise: \( u – v = \left\langle \frac{3}{4} – \frac{1}{2}, \frac{5}{6} – \frac{1}{3} \right\rangle = \left\langle \frac{1}{4}, \frac{1}{2} \right\rangle \)
Conclusion: The result of subtracting vector \( v = \left\langle \frac{1}{2}, \frac{1}{3} \right\rangle \) from vector \( u = \left\langle \frac{3}{4}, \frac{5}{6} \right\rangle \) is \( \left\langle \frac{1}{4}, \frac{1}{2} \right\rangle \). This process involves reversing the direction of the vector you want to subtract and then adding the vectors component-wise.
2D Vector Subtraction: Level 1 Example with Fractions
Given vectors \( w = \left\langle \frac{7}{8}, \frac{2}{3} \right\rangle \), \( x = \left\langle \frac{1}{4}, \frac{1}{6} \right\rangle \)
1. Write down vectors w and x: \( w = \left\langle \frac{7}{8}, \frac{2}{3} \right\rangle \), \( x = \left\langle \frac{1}{4}, \frac{1}{6} \right\rangle \)
2. Write down the negative of vector x: \( -x = \left\langle -\frac{1}{4}, -\frac{1}{6} \right\rangle \)
3. Add vector w and the negative of vector x: \( w – x = \left\langle \frac{7}{8}, \frac{2}{3} \right\rangle + \left\langle -\frac{1}{4}, -\frac{1}{6} \right\rangle \)
4. Perform the addition component-wise: \( w – x = \left\langle \frac{7}{8} – \frac{1}{4}, \frac{2}{3} – \frac{1}{6} \right\rangle = \left\langle \frac{5}{8}, \frac{1}{2} \right\rangle \)
Conclusion: The result of subtracting vector \( x = \left\langle \frac{1}{4}, \frac{1}{6} \right\rangle \) from vector \( w = \left\langle \frac{7}{8}, \frac{2}{3} \right\rangle \) is \( \left\langle \frac{5}{8}, \frac{1}{2} \right\rangle \). This process involves reversing the direction of the vector you want to subtract and then adding the vectors component-wise.
