Use the figure to find each vector: - u. Use vector notation as in Example 4.

Verified step by step guidance

1. Identify the vector \( \mathbf{u} \) from the figure, noting its direction and magnitude relative to the coordinate axes or reference points given.
2. Recall that the negative of a vector \( \mathbf{u} \), denoted \( -\mathbf{u} \), has the same magnitude as \( \mathbf{u} \) but points in the exact opposite direction.
3. Express the vector \( \mathbf{u} \) in component form, typically as \( \mathbf{u} = \langle u_x, u_y \rangle \), where \( u_x \) and \( u_y \) are the horizontal and vertical components respectively.
4. To find \( -\mathbf{u} \), multiply each component of \( \mathbf{u} \) by \( -1 \), resulting in \( -\mathbf{u} = \langle -u_x, -u_y \rangle \).
5. Write the final answer in vector notation, clearly indicating the components of \( -\mathbf{u} \) as derived from the previous step.

Key Concepts

Vector Notation

Vector notation represents vectors using components along coordinate axes, typically written as ⟨x, y⟩ in two dimensions. This notation clearly shows the direction and magnitude of the vector by specifying its horizontal and vertical components.

Vector Addition and Subtraction

Vectors can be added or subtracted by combining their corresponding components. Understanding how to perform these operations is essential for manipulating vectors and finding resultant vectors in problems involving multiple vectors.

Using Geometric Figures to Determine Vector Components

Interpreting vectors from geometric figures involves identifying their direction and length relative to coordinate axes. This skill helps translate visual information into vector notation by measuring or calculating horizontal and vertical components.