https://r2.erweima.ai/mathbot/image/1726445887859h80z2ouj.jpg

The image contains vector addition and subtraction problems. I will guide you through solving each of them step by step.

### 1. \(\vec{u} = (5, 8)\), \(\vec{v} = (2, 3)\)

#### For \(\vec{u} + \vec{v}\):
\[
\vec{u} + \vec{v} = (5 + 2, 8 + 3) = (7, 11)
\]

#### For \(\vec{u} - \vec{v}\):
\[
\vec{u} - \vec{v} = (5 - 2, 8 - 3) = (3, 5)
\]

### 2. \(\vec{u} = (3, -5)\), \(\vec{v} = (1, -1)\)

#### For \(\vec{u} + \vec{v}\):
\[
\vec{u} + \vec{v} = (3 + 1, -5 + (-1)) = (4, -6)
\]

#### For \(\vec{u} - \vec{v}\):
\[
\vec{u} - \vec{v} = (3 - 1, -5 - (-1)) = (2, -4)
\]

### 3. \(\vec{u} = (-2, 5)\), \(\vec{v} = (0, -3)\)

#### For \(\vec{u} + \vec{v}\):
\[
\vec{u} + \vec{v} = (-2 + 0, 5 + (-3)) = (-2, 2)
\]

#### For \(\vec{u} - \vec{v}\):
\[
\vec{u} - \vec{v} = (-2 - 0, 5 - (-3)) = (-2, 8)
\]

### 4. \(\vec{u} = (8, 2)\), \(\vec{v} = (10, 1)\)

#### For \(\vec{u} + \vec{v}\):
\[
\vec{u} + \vec{v} = (8 + 10, 2 + 1) = (18, 3)
\]

#### For \(\vec{u} - \vec{v}\):
\[
\vec{u} - \vec{v} = (8 - 10, 2 - 1) = (-2, 1)
\]

### 5. \(\vec{u} = (1, 5)\), \(\vec{u} + \vec{v} = (4, 7)\)

To find \(\vec{v}\), use the formula:
\[
\vec{v} = (\vec{u} + \vec{v}) - \vec{u} = (4, 7) - (1, 5)
\]

So:
\[
\vec{v} = (4 - 1, 7 - 5) = (3, 2)
\]

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Would you like more details on any of the calculations? Here are 5 related questions you can explore:

1. How can vector addition be applied in physics?
2. What is the geometric interpretation of vector subtraction?
3. How do you find the magnitude of a vector given its components?
4. What is the result of multiplying a vector by a scalar?
5. How do you calculate the dot product of two vectors?

**Tip:** Always double-check vector addition by adding components separately to avoid mistakes.

Escribe las componentes de cada vector. Completa las coordenadas de los siguientes puntos usando los datos proporcionados.

Learn how to solve vector addition and subtraction problems with examples. This includes calculating the sum and difference of two vectors and applying the commutative and associative properties. Suitable for students in Grades 9-12.

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