Math Problem Statement

Let B = 4.50 m at 60.0°. C and A have equal magnitudes. The direction angle of C is larger than that of A by 25.0°. Let A · B = 27.9 m2 and B · C = 38.1 m2. Find the magnitude (in m) and direction (in degrees) of A. magnitude

A. m direction

°

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Algebra
Dot Product
Trigonometry

Formulas

Dot product formula: A · B = |A| |B| cos(θ)
System of equations involving trigonometric identities

Theorems

Properties of the dot product

Suitable Grade Level

Undergraduate Physics or Advanced High School Mathematics (Grades 11-12)