If the position vectors of two points A and B | 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 $\vec{p} = \vec{a} + 3\vec{b}$ and $\vec{q} = \vec{a} - 2\vec{b}$.Using the section formula for

Vedclass · Accepted Answer

$\vec{a} + \frac{11}{7}\vec{b}$

Vedclass · Answer

(D) Let the position vectors of points $A$ and $B$ be $\vec{p} = \vec{a} + 3\vec{b}$ and $\vec{q} = \vec{a} - 2\vec{b}$.Using the section formula for internal division in the ratio $m:n = 2:5$,the position vector $\vec{r}$ is given by:$\vec{r} = \frac{m\vec{q} + n\vec{p}}{m + n}$Substituting the values:$\vec{r} = \frac{2(\vec{a} - 2\vec{b}) + 5(\vec{a} + 3\vec{b})}{2 + 5}$$\vec{r} = \frac{2\vec{a} - 4\vec{b} + 5\vec{a} + 15\vec{b}}{7}$$\vec{r} = \frac{7\vec{a} + 11\vec{b}}{7}$$\vec{r} = \vec{a} + \frac{11}{7}\vec{b}$

If the position vectors of two points $A$ and $B$ are $\vec{a} + 3\vec{b}$ and $\vec{a} - 2\vec{b}$ respectively,find the position vector of the point that divides $AB$ in the ratio $2:5$.

Similar Questions

If $i + 2j + 3k$ is parallel to the sum of the vectors $3i + \lambda j + 2k$ and $-2i + 3j + k$,then $\lambda = \dots$

$ABCD$ is a parallelogram and $P$ is the mid-point of the side $AD$. The line $BP$ meets the diagonal $AC$ in $Q$. Then, the ratio of $AQ:QC$ is equal to

$A$ force is a

If $\vec{a}=(p, -2, 5)$ and $\vec{b}=(1, q, -3)$ are collinear vectors,then:

If the vectors $3i - 2j + 5k$ and $-2i + pj - qk$ are collinear,then $(p, q) = $?

Vedclass Test Series

Exam Paper Generator

Online Exam Module