To find the resultant vector when adding two vectors, you need to add their corresponding components. Here's the step-by-step process:
1. Identify the components of each vector:
- Vector [tex]\(A\)[/tex] has components [tex]\( (6, 4) \)[/tex].
- Vector [tex]\(B\)[/tex] has components [tex]\( (-2, -1) \)[/tex].
2. Add the corresponding components from each vector:
- Add the [tex]\( x \)[/tex]-components of Vector [tex]\(A\)[/tex] and Vector [tex]\(B\)[/tex]:
[tex]\[
6 + (-2) = 4
\][/tex]
- Add the [tex]\( y \)[/tex]-components of Vector [tex]\(A\)[/tex] and Vector [tex]\(B\)[/tex]:
[tex]\[
4 + (-1) = 3
\][/tex]
3. Form the resultant vector from the sums of these components:
- The [tex]\( x \)[/tex]-component of the resultant vector is [tex]\( 4 \)[/tex].
- The [tex]\( y \)[/tex]-component of the resultant vector is [tex]\( 3 \)[/tex].
Therefore, the resultant vector is [tex]\( (4, 3) \)[/tex].
Matching this answer with the choices provided:
- A. [tex]\( (4, 3) \)[/tex]
- B. [tex]\( (8, 3) \)[/tex]
- C. [tex]\( (8, 5) \)[/tex]
- D. [tex]\( (4, 5) \)[/tex]
The correct answer is [tex]\( \boxed{(4, 3)} \)[/tex].
