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

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(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

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$2:3$

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(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

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