To find the sum of the vectors [tex]\( u \)[/tex] and [tex]\( v \)[/tex], we will use vector addition. When adding vectors, we add their corresponding components.
First, let's identify the components of each vector:
- Vector [tex]\( u \)[/tex] has components [tex]\( u_1 = -3 \)[/tex] and [tex]\( u_2 = 7 \)[/tex].
- Vector [tex]\( v \)[/tex] has components [tex]\( v_1 = 5 \)[/tex] and [tex]\( v_2 = 3 \)[/tex].
To find the sum [tex]\( u + v \)[/tex], we add the corresponding components of the vectors:
- The first component of the sum is given by [tex]\( u_1 + v_1 \)[/tex]:
[tex]\[
-3 + 5
\][/tex]
- The second component of the sum is given by [tex]\( u_2 + v_2 \)[/tex]:
[tex]\[
7 + 3
\][/tex]
Performing the addition, we get:
- For the first component:
[tex]\[
-3 + 5 = 2
\][/tex]
- For the second component:
[tex]\[
7 + 3 = 10
\][/tex]
Therefore, the sum of the vectors [tex]\( u \)[/tex] and [tex]\( v \)[/tex] is:
[tex]\[
u + v = \langle 2, 10 \rangle
\][/tex]
The result in component form is [tex]\(\boxed{2}\)[/tex] , [tex]\(\boxed{10}\)[/tex].
