If three points A, B, C are collinear,whose p | vedclass

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

Question

(B) Let the point $B$ divide the line segment $AC$ in the ratio $\lambda : 1$. Using the section formula,the position vector of $B$ is given by: $\vec

Vedclass · Accepted Answer

$2:3$

Vedclass · Answer

(B) Let the point $B$ divide the line segment $AC$ in the ratio $\lambda : 1$. Using the section formula,the position vector of $B$ is given by: $\vec{B} = \frac{\lambda \vec{C} + 1 \vec{A}}{\lambda + 1}$ Substituting the given position vectors: $5i - 2k = \frac{\lambda (11i + 3j + 7k) + (i - 2j - 8k)}{\lambda + 1}$ Equating the coefficients of $j$: $0 = \frac{3\lambda - 2}{\lambda + 1}$ $3\lambda - 2 = 0$ $\lambda = \frac{2}{3}$ Thus,the ratio in which $B$ divides $AC$ is $2:3$.

If three points $A, B, C$ are collinear,whose position vectors are $i - 2j - 8k$,$5i - 2k$,and $11i + 3j + 7k$ respectively,then the ratio in which $B$ divides $AC$ is

Similar Questions

Statement $(A):$ In $\Delta ABC$,$\overline{AB} + \overline{BC} + \overline{CA} = 0$.
Reason $(R):$ If $\overline{AB} = \vec{a}$ and $\overline{BC} = \vec{b}$,then $\overline{AC} = \vec{a} + \vec{b}$ (Triangle Law of Addition).

If a vector $\vec{r}$ makes equal angles with the axes $OX, OY,$ and $OZ$,find the total number of such vectors $\vec{r}$.

The position vectors of $A$ and $B$ are $2i - 9j - 4k$ and $6i - 3j + 8k$ respectively. Then the magnitude of $\overrightarrow{AB}$ is:

For given vectors,$\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}=-\hat{i}+\hat{j}-\hat{k},$ find the unit vector in the direction of the vector $\vec{a}+\vec{b}.$

If $P(1, 3, -7)$ and $Q(5, -2, 4)$,then $|\vec{PQ}| = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module