Find the position vector of a point R which d | vedclass

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

Question

(A) The position vector of point $R$ dividing the line segment joining two points $P$ and $Q$ with position vectors $\vec{a}$ and $\vec{b}$ in the rat

Vedclass · Accepted Answer

$-3 \hat{i}+3 \hat{k}$

Vedclass · Answer

(A) The position vector of point $R$ dividing the line segment joining two points $P$ and $Q$ with position vectors $\vec{a}$ and $\vec{b}$ in the ratio $m: n$ externally is given by: $\vec{r} = \frac{m \vec{b} - n \vec{a}}{m - n}$.Given position vectors are $\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} + \hat{k}$ with ratio $m: n = 2: 1$.Substituting the values into the formula:$\vec{r} = \frac{2(-\hat{i} + \hat{j} + \hat{k}) - 1(\hat{i} + 2 \hat{j} - \hat{k})}{2 - 1}$$= \frac{-2 \hat{i} + 2 \hat{j} + 2 \hat{k} - \hat{i} - 2 \hat{j} + \hat{k}}{1}$$= -3 \hat{i} + 3 \hat{k}$.

Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $\hat{i}+2 \hat{j}-\hat{k}$ and $-\hat{i}+\hat{j}+\hat{k}$ respectively,in the ratio $2: 1$ externally.

Similar Questions

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

The non-zero vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$. Then the angle between $\vec{a}$ and $\vec{c}$ is ............... $^\circ $

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 points $P(4, 5, x)$,$Q(3, y, 4)$ and $R(5, 8, 0)$ are collinear,then the value of $x + y$ is

If non-zero vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$,find the angle between $\vec{a}$ and $\vec{c}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module