To find the sum of the given vectors [tex]\( u =\langle-7,-2\rangle \)[/tex] and [tex]\( v =\langle 5,-2\rangle \)[/tex], we need to add them component-wise.
### Step-by-Step Solution:
1. Identify the components of each vector:
- Vector [tex]\( u \)[/tex] has components [tex]\( u_1 = -7 \)[/tex] and [tex]\( u_2 = -2 \)[/tex].
- Vector [tex]\( v \)[/tex] has components [tex]\( v_1 = 5 \)[/tex] and [tex]\( v_2 = -2 \)[/tex].
2. Add the corresponding components of the two vectors:
- For the first component: [tex]\( u_1 + v_1 = -7 + 5 \)[/tex]
- For the second component: [tex]\( u_2 + v_2 = -2 + (-2) \)[/tex]
3. Perform the arithmetic operations:
- First component sum: [tex]\( -7 + 5 = -2 \)[/tex]
- Second component sum: [tex]\( -2 + (-2) = -4 \)[/tex]
4. Combine the results into a new vector:
- The sum of the vectors [tex]\( u \)[/tex] and [tex]\( v \)[/tex] is [tex]\( \langle -2, -4 \rangle \)[/tex].
So, the sum [tex]\( u + v \)[/tex] in component form is [tex]\( \langle -2, -4 \rangle \)[/tex].
### Final Answer:
[tex]\[
\boxed{\langle -2, -4 \rangle}
\][/tex]
