Math Problem Statement
There are 3 vectors in a 2D coordinate with unit vector π₯Μ and π¦Μ along x and y axes respectively. The magnitude of πβ is 5 and it forms an angle of 60π with the positive x-axis. Vector πββ = 5π₯Μ + 8π¦Μ. The coordinates of the starting and ending points of πβ are (4, 5) and (12, 7). Calculate the resultant of πβ + πββ + πβ
Solution
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Math Problem Analysis
Mathematical Concepts
Vector addition
Trigonometry
Pythagorean theorem
Coordinate geometry
Formulas
Vector components: a_x = magnitude * cos(angle), a_y = magnitude * sin(angle)
Resultant vector magnitude: |R| = β(R_x^2 + R_y^2)
Theorems
Pythagorean theorem
Suitable Grade Level
Grades 10-12
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