Math Problem Statement

Vector #1: 202 at 270°

Vector #2: 421 at 0°

What is the magnitude and absolute angle of the resultant vector?

Solution

To find the magnitude and absolute angle of the resultant vector, we need to break down each vector into its components, sum these components, and then calculate the magnitude and direction of the resultant vector.

Given:

  • Vector #1: Magnitude = 202, Angle = 270°
  • Vector #2: Magnitude = 421, Angle = 0°

Step 1: Break down each vector into its components.

  • Vector #1 Components: x1=202×cos(270)=202×0=0x_1 = 202 \times \cos(270^\circ) = 202 \times 0 = 0 y1=202×sin(270)=202×(1)=202y_1 = 202 \times \sin(270^\circ) = 202 \times (-1) = -202

  • Vector #2 Components: x2=421×cos(0)=421×1=421x_2 = 421 \times \cos(0^\circ) = 421 \times 1 = 421 y2=421×sin(0)=421×0=0y_2 = 421 \times \sin(0^\circ) = 421 \times 0 = 0

Step 2: Sum the components to get the resultant vector

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Math Problem Analysis

Mathematical Concepts

Vectors
Trigonometry
Component Addition

Formulas

Vector components using trigonometric functions

Theorems

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Suitable Grade Level

Grades 11-12