Magnitude: ≈ 1 0 2 . 1 N Direction: 2 2 5 . 1 ° measured counterclockwise from the positive x – axis

Answer

Vector Analysis: 102.1 N at 225.1° – Full Explanation

📐 Vector Analysis: Magnitude ≈ 102.1 N at 225.1°

🔹 What is a Vector?

In physics and mathematics, a vector is a quantity that has both magnitude (size) and direction. Forces, velocities, and accelerations are examples of vector quantities.

This particular vector has:

Magnitude: ≈ 102.1 Newtons (N)
Direction: 225.1° measured counterclockwise from the positive x-axis

🔹 Understanding the Direction

An angle of 225.1° lies in the third quadrant of the Cartesian coordinate plane. This means both the x and y components of the vector will be negative.

Here’s a visual interpretation:

0° = Positive x-axis (→)
90° = Positive y-axis (↑)
180° = Negative x-axis (←)
225.1° = In between 180° and 270°, pointing down-left

🔹 Resolving the Vector into Components

To analyze this vector further, we resolve it into its horizontal (x) and vertical (y) components using trigonometric formulas:

X = R × cos(θ)
Y = R × sin(θ)

Where:

R = Magnitude of the vector = 102.1 N
θ = 225.1°

📊 Calculated Components:

      cos(225.1°) ≈ -0.7078

      sin(225.1°) ≈ -0.7064

X Component ≈ 102.1 × (−0.7078) ≈ −72.29 N
Y Component ≈ 102.1 × (−0.7064) ≈ −72.17 N

🔹 Final Interpretation

The force vector can be described as pointing in the southwest direction, since both x and y components are negative. It indicates that the force is acting:

🌐 72.29 N toward the negative x-axis (left)
🌐 72.17 N toward the negative y-axis (down)

      📌 This kind of vector is commonly seen in real-world physics problems involving inclined planes, projectile motion, or wind forces.
    

🔹 Summary

🎯 Magnitude: 102.1 N
🎯 Direction: 225.1° from positive x-axis
📉 X Component: –72.29 N
📉 Y Component: –72.17 N
📌 Quadrant: Third (Southwest direction)

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