Let the angle between two nonzero vectors ove | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is $	heta = 120^{\circ}$.The magnitude of the resultant $\overrightarr

Vedclass · Accepted Answer

$\overrightarrow{C}$ must be less than $|\overrightarrow{A} - \overrightarrow{B}|$

Vedclass · Answer

(C) Given that the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is $	heta = 120^{\circ}$.The magnitude of the resultant $\overrightarrow{C} = \overrightarrow{A} + \overrightarrow{B}$ is given by:$|\overrightarrow{C}| = \sqrt{A^{2} + B^{2} + 2AB \cos 120^{\circ}} = \sqrt{A^{2} + B^{2} - AB}$.The magnitude of the difference vector $|\overrightarrow{A} - \overrightarrow{B}|$ is given by:$|\overrightarrow{A} - \overrightarrow{B}| = \sqrt{A^{2} + B^{2} - 2AB \cos 120^{\circ}} = \sqrt{A^{2} + B^{2} - 2AB (-1/2)} = \sqrt{A^{2} + B^{2} + AB}$.Comparing the two expressions,since $A$ and $B$ are nonzero magnitudes,$\sqrt{A^{2} + B^{2} - AB} Therefore,$|\overrightarrow{C}| < |\overrightarrow{A} - \overrightarrow{B}|$.

Let the angle between two nonzero vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ be $120^{\circ}$ and their resultant be $\overrightarrow{C}$. Which of the following is true?

Similar Questions

Two forces of magnitude $8 \, N$ and $15 \, N$ respectively act at a point. If the resultant force is $17 \, N$,the angle between the forces is: (in $^{\circ}$)

What is the meaning of subtraction of two vectors?

$A$ car travels a distance of $6 \, km$ at an angle of $45^\circ$ with the East,and then travels a distance of $4 \, km$ at an angle of $135^\circ$ with the East. What is the distance from the origin?

$A$ truck travelling due north at $20 \, m/s$ turns west and travels at the same speed. The change in its velocity is

The magnitudes of vectors $\overrightarrow{A}$,$\overrightarrow{B}$,and $\overrightarrow{C}$ are $12$,$5$,and $13$ units respectively,and $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$. Then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module