The figure shows three vectors vec{a}, vec{b} | vedclass

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

Question

(A) Step $1$: Applying the triangle law of vector addition.In $	riangle OPR$,by the triangle law of vector addition:$\vec{a} = \vec{c} + \overrightar

Vedclass · Accepted Answer

$\vec{a} + \vec{b} = 2\vec{c}$

Vedclass · Answer

(A) Step $1$: Applying the triangle law of vector addition.In $	riangle OPR$,by the triangle law of vector addition:$\vec{a} = \vec{c} + \overrightarrow{RP} \quad (1)$In $	riangle ORQ$,by the triangle law of vector addition:$\vec{b} = \overrightarrow{RQ} - \vec{c} \implies \vec{c} + \vec{b} = \overrightarrow{RQ} \implies \vec{b} = \overrightarrow{RQ} - \vec{c}$ (Wait,let's re-evaluate the geometry).Correct approach: In $	riangle OPR$,$\vec{a} = \vec{c} + \overrightarrow{RP}$.In $	riangle ORQ$,$\vec{c} = \vec{b} + \overrightarrow{RQ} \implies \overrightarrow{RQ} = \vec{c} - \vec{b}$.Since $R$ is the midpoint of $PQ$,$\overrightarrow{PR} + \overrightarrow{RQ} = 0$,so $\overrightarrow{RP} = -\overrightarrow{RQ}$.From $	riangle OPR$,$\overrightarrow{RP} = \vec{a} - \vec{c}$.From $	riangle ORQ$,$\overrightarrow{RQ} = \vec{c} - \vec{b}$.Since $\overrightarrow{RP} + \overrightarrow{RQ} = 0$,we have $(\vec{a} - \vec{c}) + (\vec{c} - \vec{b}) = 0$ is incorrect. Let's use position vectors.Let origin be $O$. Then $\vec{a} = \vec{P}$,$\vec{b} = \vec{Q}$,$\vec{c} = \vec{R}$.Since $R$ is the midpoint of $PQ$,$\vec{R} = \frac{\vec{P} + \vec{Q}}{2}$.Therefore,$\vec{c} = \frac{\vec{a} + \vec{b}}{2}$,which implies $\vec{a} + \vec{b} = 2\vec{c}$.

The figure shows three vectors $\vec{a}, \vec{b}$ and $\vec{c}$,where $R$ is the midpoint of $PQ$. Which of the following relations is correct?

Similar Questions

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 $^{\circ}$)

$A$ unit vector in the direction of the resultant vector of $\vec{A} = -2 \hat{i} + 3 \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} - 4 \hat{k}$ is

If the sum of two unit vectors is a unit vector,find the magnitude of their difference.

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?

$A$ vector $\vec{A}$ when added to the sum of the vectors $(\hat{i} - 2\hat{j} + 2\hat{k})$ and $(-2\hat{i} + \hat{j} - \hat{k})$ gives a unit vector along the $Y$-axis. The magnitude of vector $\vec{A}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module