Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Addition and Subtraction
Vector Magnitudes
Parallel Vectors
Unit Vectors
Vector Components
Direction Angles

Formulas

Vector Magnitude: |a| = sqrt(a1^2 + a2^2)
Vector Addition/Subtraction: a ± b = (a1 ± b1)i + (a2 ± b2)j
Unit Vector: â = a / |a|
Dot Product: a ⋅ b = |a||b|cos(θ)

Theorems

Pythagorean Theorem for vector magnitude
Law of Cosines for direction angle
Dot Product and Parallelism

Suitable Grade Level

University level, Engineering Mathematics