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

step 1 In this question we will learn about some basic concept of the vectors. The question is, there a

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

Two forces $\vec{F}_{2}=500 \mathrm{~N}$ 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 $\vec{F}_{2}=500 \mathrm{~N}$ 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 of a Vector

Determining the direction of a vector typically involves calculating the angle it makes with a reference axis. This is often done using trigonometric functions, such as the inverse tangent, which provides the angle based on the ratio of the vertical component to the horizontal component.

Magnitude of a Resultant Vector

The magnitude of a resultant vector is found by combining the components using the Pythagorean theorem. After performing vector subtraction or addition, the overall size of the resultant force is determined from the square root of the sum of the squares of its individual components.

Component Resolution of Vectors

Component resolution involves breaking a vector into its horizontal and vertical components, usually along the x- and y-axes. This process simplifies the manipulation of vectors, such as addition or subtraction, by allowing operations to be performed on each component independently.

Vector Subtraction

Vector subtraction is a method of finding the difference between two vectors by subtracting their corresponding components. This concept is crucial in mechanics and physics for determining how one force compares to another in both magnitude and direction.

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