Math Problem Statement

Two vectors \( \vec{A} \) and \( \vec{B} \) are given, where \( |\vec{A}| = 4 \, \text{m} \) and \( |\vec{B}| = 5 \, \text{m} \). The angle between these two vectors is \( 60^\circ \). The task is to calculate \( |\vec{A} + \vec{B}| \), the magnitude of the resultant vector.

Solution

The image contains a problem related to vector magnitudes and their angle.

The problem appears to be:

  • Two vectors A\vec{A} and B\vec{B} are given, where A=4m|\vec{A}| = 4 \, \text{m} and B=5m|\vec{B}| = 5 \, \text{m}.
  • The angle between these two vectors is 6060^\circ.
  • The task is to calculate A+B|\vec{A} + \vec{B}|, the magnitude of the resultant vector.

The formula for the magnitude of the resultant vector A+B\vec{A} + \vec{B} is: A+B=A2+B2+2ABcos(θ)|\vec{A} + \vec{B}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}|\cos(\theta)} where:

  • A=4m|\vec{A}| = 4 \, \text{m},
  • B=5m|\vec{B}| = 5 \, \text{m},
  • θ=60\theta = 60^\circ.

Let me calculate the magnitude.

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Math Problem Analysis

Mathematical Concepts

Vectors
Vector Magnitude
Vector Addition

Formulas

Magnitude of resultant vector: \( |\vec{A} + \vec{B}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}|\cos(\theta)} \)

Theorems

Cosine Rule for Vectors

Suitable Grade Level

Grades 10-12