Two forces of F⃗1=500 N due east and F⃗2=250 N due north have their common initial point. F⃗2-

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Two forces of F⃗1=500 N due east and F⃗2=250 N due north...

Two forces of $\vec{F}_{1}=500 \mathrm{~N}$ due east and $\vec{F}_{2}=250 \mathrm{~N}$ due north have their common initial point. $\vec{F}_{2}-\vec{F}_{1}$ is a. $250 \sqrt{5} \mathrm{~N}, \tan ^{-1}(2) \mathrm{W}$ of $\mathrm{N}$ b. $250 \mathrm{~N}, \tan ^{-1}(2) \mathrm{W}$ of $\mathrm{N}$ c. zero d. $750 \mathrm{~N}, \tan ^{-1}(3 / 4) \mathrm{N}$ of $\mathrm{W}$

Two forces of $\vec{F}_{1}=500 \mathrm{~N}$ due east and $\vec{F}_{2}=250 \mathrm{~N}$ due north have their common initial point. $\vec{F}_{2}-\vec{F}_{1}$ is
a. $250 \sqrt{5} \mathrm{~N}, \tan ^{-1}(2) \mathrm{W}$ of $\mathrm{N}$
b. $250 \mathrm{~N}, \tan ^{-1}(2) \mathrm{W}$ of $\mathrm{N}$
c. zero
d. $750 \mathrm{~N}, \tan ^{-1}(3 / 4) \mathrm{N}$ of $\mathrm{W}$

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Key Concepts

Direction Determination

Direction determination involves finding the angle a vector makes with a reference axis, typically using inverse trigonometric functions such as the arctan. Accurately calculating the direction is crucial in many fields, as it influences the resultant vector's orientation relative to standard coordinate directions.

Magnitude Calculation

The magnitude of a vector is the length or size of the vector and can be determined using the Pythagorean theorem when the vector is expressed in its component form. Calculating the magnitude is essential in quantifying the overall effect or intensity of the vector in various applications.

Vector Subtraction

Vector subtraction involves finding a new vector that represents the difference between two vectors by subtracting their corresponding components. This operation is fundamental in understanding relative directions and magnitudes in physics and engineering, and is often visualized by placing the vectors tail-to-tail or tip-to-tail in a diagram.

Component Analysis

Component analysis breaks down a vector into its orthogonal parts, typically along the horizontal (x-axis) and vertical (y-axis) directions. This technique simplifies operations like addition and subtraction by allowing each dimension to be handled separately, providing clarity in analyzing the overall vector behavior.

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