The xy-plane divides the line segment joining | vedclass

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(C) Let the $xy$-plane divide the line segment joining the points $A(-1, 3, 4)$ and $B(2, -5, 6)$ in the ratio $\lambda : 1$.The coordinates of the po

Vedclass · Accepted Answer

Externally in the ratio $2 : 3$

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(C) Let the $xy$-plane divide the line segment joining the points $A(-1, 3, 4)$ and $B(2, -5, 6)$ in the ratio $\lambda : 1$.The coordinates of the point of division are given by the section formula:$P = \left( \frac{2\lambda - 1}{\lambda + 1}, \frac{-5\lambda + 3}{\lambda + 1}, \frac{6\lambda + 4}{\lambda + 1} \right)$Since the point lies on the $xy$-plane,its $z$-coordinate must be $0$:$\frac{6\lambda + 4}{\lambda + 1} = 0$Solving for $\lambda$:$6\lambda + 4 = 0$$6\lambda = -4$$\lambda = -\frac{4}{6} = -\frac{2}{3}$Since $\lambda$ is negative,the division is external in the ratio $2 : 3$.

The $xy$-plane divides the line segment joining the points $(-1, 3, 4)$ and $(2, -5, 6)$ in which ratio?

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