(B) The angle between vector $\vec{A}$ and vector $\vec{B}$ is $\theta = 110^\circ - 20^\circ = 90^\circ$.The magnitude of the resultant vector $R$ is

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(B) The angle between vector $\vec{A}$ and vector $\vec{B}$ is $\theta = 110^\circ - 20^\circ = 90^\circ$.The magnitude of the resultant vector $R$ is given by the formula:$R = \sqrt{A^2 + B^2 + 2AB \cos \theta}$Substituting the given values $A = 5 \, m$,$B = 12 \, m$,and $\theta = 90^\circ$:$R = \sqrt{5^2 + 12^2 + 2(5)(12) \cos 90^\circ}$Since $\cos 90^\circ = 0$:$R = \sqrt{25 + 144 + 0} = \sqrt{169} = 13 \, m$.Thus,the magnitude of the resultant vector is $13 \, m$.

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

Medium

Vectors $\vec{A}$ and $\vec{B}$ make angles of $20^\circ$ and $110^\circ$ with the $X$-axis,respectively. The magnitudes of these vectors are $5 \, m$ and $12 \, m$,respectively. The magnitude of the resultant vector of these two vectors is ....... $m$.

A
$11$
B
$13$
C
$17$
D
$19$

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3-1.Vectors

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Addition and Subtraction of Vectors

The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q} + 2 \vec{P})$ and $(2 \vec{Q} - 2 \vec{P})$ is:

MediumJEE MAIN 2024

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If $|A|=2$ and $|B|=4$ and the angle between them is $60^{\circ}$,then $|A-B|$ is

Medium

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The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . . (in $^{\circ}$)

DifficultJEE MAIN 2024

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If $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}$,$\vec{B}=\hat{i}-3 \hat{j}+5 \hat{k}$ and $\vec{C}=2 \hat{i}+\hat{j}-4 \hat{k}$ form a right-angled triangle,then which of the following is satisfied?

MediumMHT CET 2018

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Two forces whose magnitudes are in the ratio $5:3$ are acting at a point at an angle $60^{\circ}$ simultaneously. If the resultant of the two forces is $35 \ N$,then the magnitudes of the two forces respectively are

EasyAP EAMCET 2023

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Vectors $\vec{A}$ and $\vec{B}$ make angles of $20^\circ$ and $110^\circ$ with the $X$-axis,respectively. The magnitudes of these vectors are $5 \, m$ and $12 \, m$,respectively. The magnitude of the resultant vector of these two vectors is ....... $m$.

Similar Questions

The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q} + 2 \vec{P})$ and $(2 \vec{Q} - 2 \vec{P})$ is:

If $|A|=2$ and $|B|=4$ and the angle between them is $60^{\circ}$,then $|A-B|$ is

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . . (in $^{\circ}$)

If $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}$,$\vec{B}=\hat{i}-3 \hat{j}+5 \hat{k}$ and $\vec{C}=2 \hat{i}+\hat{j}-4 \hat{k}$ form a right-angled triangle,then which of the following is satisfied?

Two forces whose magnitudes are in the ratio $5:3$ are acting at a point at an angle $60^{\circ}$ simultaneously. If the resultant of the two forces is $35 \ N$,then the magnitudes of the two forces respectively are

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