 Vector A has a magnitude of 63 units and points due west, while vector B has the same magnitude and points due south. Find the magnitude and direction of (a) A + B and (b) AB. Specify the directions relative to due west. 

Let's break down the problem and solve it step by step.

### (a) Finding the Magnitude and Direction of \( \mathbf{A} + \mathbf{B} \)

Given:
- Vector \(\mathbf{A}\) has a magnitude of 63 units and points due west.
- Vector \(\mathbf{B}\) has a magnitude of 63 units and points due south.

#### Step 1: Represent the vectors in component form

1. **Vector \(\mathbf{A}\):**  
   Since \(\mathbf{A}\) points due west, it has no vertical component (i.e., its \(y\)-component is 0), and its \(x\)-component is \(-63\) (negative because it points west).  
   \[
   \mathbf{A} = \langle -63, 0 \rangle
   \]

2. **Vector \(\mathbf{B}\):**  
   Since \(\mathbf{B}\) points due south, it has no horizontal component (i.e., its \(x\)-component is 0), and its \(y\)-component is \(-63\) (negative because it points south).  
   \[
   \mathbf{B} = \langle 0, -63 \rangle
   \]

#### Step 2: Add the vectors

The resultant vector \(\mathbf{R} = \mathbf{A} + \mathbf{B}\) is calculated by adding the corresponding components of \(\mathbf{A}\) and \(\mathbf{B}\):
\[
\mathbf{R} = \mathbf{A} + \mathbf{B} = \langle -63, 0 \

Explore how to solve a vector addition problem involving vectors pointing due west and due south. Understand how to calculate the magnitude and direction of the resultant vector. Suitable for Grades 11-12.

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