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

If $a, b, c$ are any vectors,then the true statement is

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

Compute the magnitude of the following vectors:
$\vec{a}=\hat{i}+\hat{j}+\hat{k} ; \quad \vec{b}=2 \hat{i}-7 \hat{j}-3 \hat{k} ; \quad \vec{c}=\frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}-\frac{1}{\sqrt{3}} \hat{k}$

The magnitude of the sum of vectors $(1, -\sqrt{2})$ and $(2, \sqrt{2})$ is $\ldots$

If $|\overline{u}|=2$ and $\overline{u}$ makes angles of $60^{\circ}$ and $120^{\circ}$ with axes $OX$ and $OY$ respectively,then $\overline{u}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module