A point C with position vector frac{3 bar{a}+ | vedclass

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

Question

(D) Let the position vectors of points $A$ and $B$ be $\vec{r}_A$ and $\vec{r}_B$ respectively.Given $\vec{r}_A = \bar{a}-2 \bar{b}+3 \bar{c}$.Point $

Vedclass · Accepted Answer

$\bar{a}+3 \bar{b}-4 \bar{c}$

Vedclass · Answer

(D) Let the position vectors of points $A$ and $B$ be $\vec{r}_A$ and $\vec{r}_B$ respectively.Given $\vec{r}_A = \bar{a}-2 \bar{b}+3 \bar{c}$.Point $C$ divides the line segment $AB$ in the ratio $m:n = 2:1$.The position vector of $C$ is given by the section formula: $\vec{r}_C = \frac{m \vec{r}_B + n \vec{r}_A}{m+n}$.Substituting the given values: $\frac{3 \bar{a}+4 \bar{b}-5 \bar{c}}{3} = \frac{2 \vec{r}_B + 1 (\bar{a}-2 \bar{b}+3 \bar{c})}{2+1}$.$\frac{3 \bar{a}+4 \bar{b}-5 \bar{c}}{3} = \frac{2 \vec{r}_B + \bar{a}-2 \bar{b}+3 \bar{c}}{3}$.Equating the numerators: $3 \bar{a}+4 \bar{b}-5 \bar{c} = 2 \vec{r}_B + \bar{a}-2 \bar{b}+3 \bar{c}$.$2 \vec{r}_B = (3 \bar{a}-\bar{a}) + (4 \bar{b}+2 \bar{b}) + (-5 \bar{c}-3 \bar{c})$.$2 \vec{r}_B = 2 \bar{a} + 6 \bar{b} - 8 \bar{c}$.$\vec{r}_B = \bar{a} + 3 \bar{b} - 4 \bar{c}$.Thus,the position vector of $B$ is $\bar{a} + 3 \bar{b} - 4 \bar{c}$.

Similar Questions

Let $\alpha, \beta, \gamma$ be distinct real numbers. The points with position vectors $\alpha \hat{i} + \beta \hat{j} + \gamma \hat{k}$,$\beta \hat{i} + \gamma \hat{j} + \alpha \hat{k}$,and $\gamma \hat{i} + \alpha \hat{j} + \beta \hat{k}$:

If the vectors $3\,i + 2\,j - k$ and $6\,i - 4xj + yk$ are parallel,then the value of $x$ and $y$ will be

If the angle between $\vec{a}$ and $\vec{b}$ is $30^o$,then the angle between $3\vec{a}$ and $-4\vec{b}$ will be ............ $^o$.

Classify the following measure as a scalar or a vector:
$10^{-19} \text{ Coulomb}$

If $C$ is the midpoint of $\overline{AB}$ and $P$ is any point not on $\overline{AB}$,then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module