To determine [tex]\( A - B \)[/tex] for the given vectors [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we need to follow the steps for vector subtraction.
Given:
[tex]\[ A = (3, 0) \][/tex]
[tex]\[ B = (-3, 3) \][/tex]
### Step-by-Step Solution:
1. Identify the components of each vector:
- Vector [tex]\( A \)[/tex] has components [tex]\( (3, 0) \)[/tex]: [tex]\( A_x = 3 \)[/tex] and [tex]\( A_y = 0 \)[/tex].
- Vector [tex]\( B \)[/tex] has components [tex]\( (-3, 3) \)[/tex]: [tex]\( B_x = -3 \)[/tex] and [tex]\( B_y = 3 \)[/tex].
2. Subtract the components of vector [tex]\( B \)[/tex] from vector [tex]\( A \)[/tex]:
- For the x-component: [tex]\( A_x - B_x = 3 - (-3) \)[/tex]
- For the y-component: [tex]\( A_y - B_y = 0 - 3 \)[/tex]
3. Perform the calculations:
- [tex]\( 3 - (-3) = 3 + 3 = 6 \)[/tex]
- [tex]\( 0 - 3 = -3 \)[/tex]
4. Write the result as a vector:
- The resulting vector from [tex]\( A - B \)[/tex] is [tex]\( (6, -3) \)[/tex].
Thus, the vector [tex]\( A - B \)[/tex] is [tex]\((6, -3)\)[/tex].
### Conclusion:
The correct option that matches the result [tex]\((6, -3)\)[/tex] is:
A. (6, -3)
