Let vec{p} and vec{q} be the position vectors | vedclass

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

Question

(A) Let $\vec{r}$ and $\vec{s}$ be the position vectors of points $R$ and $S$ respectively.Using the section formula for internal division in ratio $2

Vedclass · Accepted Answer

$9p^2 = 4q^2$

Vedclass · Answer

(A) Let $\vec{r}$ and $\vec{s}$ be the position vectors of points $R$ and $S$ respectively.Using the section formula for internal division in ratio $2:3$:$\vec{r} = \frac{2\vec{q} + 3\vec{p}}{2+3} = \frac{3\vec{p} + 2\vec{q}}{5}$Using the section formula for external division in ratio $2:3$:$\vec{s} = \frac{2\vec{q} - 3\vec{p}}{2-3} = \frac{2\vec{q} - 3\vec{p}}{-1} = 3\vec{p} - 2\vec{q}$Since $\vec{OR}$ and $\vec{OS}$ are perpendicular,their dot product is zero:$\vec{r} \cdot \vec{s} = 0$$\left(\frac{3\vec{p} + 2\vec{q}}{5}\right) \cdot (3\vec{p} - 2\vec{q}) = 0$$(3\vec{p} + 2\vec{q}) \cdot (3\vec{p} - 2\vec{q}) = 0$$9|\vec{p}|^2 - 6(\vec{p} \cdot \vec{q}) + 6(\vec{q} \cdot \vec{p}) - 4|\vec{q}|^2 = 0$$9p^2 - 4q^2 = 0$$9p^2 = 4q^2$

Similar Questions

The set of all real values of $c$ such that the angle between the vectors $\vec{a} = cx \hat{i} - 6 \hat{j} + 3 \hat{k}$ and $\vec{b} = x \hat{i} + 2 \hat{j} + 2cx \hat{k}$ is an obtuse angle for all real $x$ is:

If the vectors $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$,$\vec{b} = 2\hat{i} + 4\hat{j} + \hat{k}$,and $\vec{c} = \alpha\hat{i} + \hat{j} + \beta\hat{k}$ are mutually orthogonal,then $(\alpha, \beta) = $

If the projection of $\bar{a}$ on $\bar{b}+\bar{c}$ is twice the projection of $\bar{b}+\bar{c}$ on $\bar{a}$,and if $|\bar{b}|=2 \sqrt{2}$,$|\bar{c}|=4$,and the angle between $\bar{b}$ and $\bar{c}$ is $\frac{\pi}{4}$,then $|\bar{a}|=$

If $a, b, c$ are coplanar vectors,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module