## Math Problem Statement

Let B = 5.00 m at 42.0 ◦ . Let the vector C have the same magnitude as A and a direction angle greater than that of A by 𝛿 = 20.0 ◦ . We know that A · B = 28.0 m2 and B · C = 32.0 m2 . A. (2 points) What is the angle between A and B? B. (4 points) What is the magnitude and direction of A?

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Vector Algebra

Dot Product

Trigonometry

### Formulas

Dot Product: A · B = |A| |B| cos(θ)

Cosine of Angle: cos(θ) = (A · B) / (|A| |B|)

### Theorems

Dot Product Theorem

Cosine Rule

### Suitable Grade Level

College-level Physics or Mathematics

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