(C) When two vectors act at an angle $\theta$ to each other,their resultant magnitude is given by the formula $R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos

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(C) When two vectors act at an angle $\theta$ to each other,their resultant magnitude is given by the formula $R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos \theta}$.Since the forces are mutually perpendicular,the angle between them is $\theta = 90^\circ$.Substituting $\cos 90^\circ = 0$ into the formula:$R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2(0)}$$R = \sqrt{F_1^2 + F_2^2}$.Therefore,the correct option is $C$.

Class 11 Physics 3-1.Vectors Addition and Subtraction of Vectors

Easy

Forces $F_1$ and $F_2$ act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be

A
$F_1 + F_2$
B
$F_1 - F_2$
C
$\sqrt{F_1^2 + F_2^2}$
D
$F_1^2 + F_2^2$

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3-1.Vectors

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Addition and Subtraction of Vectors

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

DifficultAIIMS 2019

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The sum of the magnitudes of two forces is $25 \,N$. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $10 \,N$. The two forces are:

DifficultTS EAMCET 2015

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Explain the triangle method (head-to-tail method) of vector addition.

Medium

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$A$ body moves due East with a velocity of $20 \, km/h$ and then due North with a velocity of $15 \, km/h$. The resultant velocity is .......... $km/h$.

Easy

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Two vectors of equal magnitude $5$ units have an angle $60^\circ$ between them. Find the magnitude of $(a)$ the sum of the vectors and $(b)$ the difference of the vectors.

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Forces $F_1$ and $F_2$ act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be

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The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

The sum of the magnitudes of two forces is $25 \,N$. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $10 \,N$. The two forces are:

Explain the triangle method (head-to-tail method) of vector addition.

$A$ body moves due East with a velocity of $20 \, km/h$ and then due North with a velocity of $15 \, km/h$. The resultant velocity is .......... $km/h$.

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