The line joining points (3, 5, -7) and (-2, 1 | vedclass

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Question

(A) Let the $yz$-plane divide the line segment joining the points $A(3, 5, -7)$ and $B(-2, 1, 8)$ in the ratio $\lambda : 1$. Since the point lies on

Vedclass · Accepted Answer

$\left(0, \frac{13}{5}, 2\right)$

Vedclass · Answer

(A) Let the $yz$-plane divide the line segment joining the points $A(3, 5, -7)$ and $B(-2, 1, 8)$ in the ratio $\lambda : 1$. Since the point lies on the $yz$-plane,its $x$-coordinate must be $0$. Using the section formula for the $x$-coordinate: $\frac{\lambda(-2) + 1(3)}{\lambda + 1} = 0$ $-2\lambda + 3 = 0 \Rightarrow \lambda = \frac{3}{2}$. Thus,the ratio is $3 : 2$. Now,find the $y$ and $z$ coordinates using the ratio $3 : 2$: $y = \frac{3(1) + 2(5)}{3 + 2} = \frac{3 + 10}{5} = \frac{13}{5}$ $z = \frac{3(8) + 2(-7)}{3 + 2} = \frac{24 - 14}{5} = \frac{10}{5} = 2$ Therefore,the required point is $\left(0, \frac{13}{5}, 2\right)$.

The line joining points $(3, 5, -7)$ and $(-2, 1, 8)$ meets the $yz$-plane at which point?

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