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If Vector A is [tex]$(3,0)$[/tex] and Vector B is [tex]$(-3,3)$[/tex], what is [tex][tex]$A - B$[/tex][/tex]?

A. [tex]$(6,-3)$[/tex]
B. [tex]$(0,0)$[/tex]
C. [tex][tex]$(-3,3)$[/tex][/tex]
D. [tex]$(6,3)$[/tex]

Sagot :

GinnyAnsweridn
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)
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