The coordinates of the point at which the XZ- | vedclass

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

Question

(B) Let the $XZ$-plane divide the line segment joining $A(-2, 3, 4)$ and $B(1, 2, 3)$ in the ratio $k:1$ at point $P$. Since the point $P$ lies on the

Vedclass · Accepted Answer

$(7, 0, 1)$

Vedclass · Answer

(B) Let the $XZ$-plane divide the line segment joining $A(-2, 3, 4)$ and $B(1, 2, 3)$ in the ratio $k:1$ at point $P$. Since the point $P$ lies on the $XZ$-plane,its $y$-coordinate must be $0$. The coordinates of $P$ are given by the section formula: $P = \left( \frac{k(1) + 1(-2)}{k+1}, \frac{k(2) + 1(3)}{k+1}, \frac{k(3) + 1(4)}{k+1} \right)$. Setting the $y$-coordinate to $0$: $\frac{2k + 3}{k+1} = 0 \implies 2k + 3 = 0 \implies k = -\frac{3}{2}$. Now,substitute $k = -\frac{3}{2}$ into the $x$ and $z$ coordinates: $x = \frac{-\frac{3}{2}(1) - 2}{-\frac{3}{2} + 1} = \frac{-\frac{7}{2}}{-\frac{1}{2}} = 7$. $z = \frac{-\frac{3}{2}(3) + 4}{-\frac{3}{2} + 1} = \frac{-\frac{9}{2} + 4}{-\frac{1}{2}} = \frac{-\frac{1}{2}}{-\frac{1}{2}} = 1$. Thus,the coordinates of the point are $(7, 0, 1)$.

The coordinates of the point at which the $XZ$-plane divides the line segment joining $A(-2, 3, 4)$ and $B(1, 2, 3)$ are:

Similar Questions

If the shortest distance between the lines $\frac{x-\lambda}{2}=\frac{y-4}{3}=\frac{z-3}{4}$ and $\frac{x-2}{4}=\frac{y-4}{6}=\frac{z-7}{8}$ is $\frac{13}{\sqrt{29}}$,then a value of $\lambda$ is :

The point of intersection of the lines represented by $r=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})$ and $r=(-\hat{i}-3 \hat{j}+7 \hat{k})+\mu(\hat{i}+2 \hat{j}-\hat{k})$ is

If the points $A(-1, 3, 2)$,$B(-4, 2, -2)$,and $C(5, 5, \lambda)$ are collinear,then $\lambda = $

The coordinates of the foot of the perpendicular from the point $(1, 0, 0)$ to the line $\frac{x - 1}{2} = \frac{y + 1}{-3} = \frac{z + 10}{8}$ are

$A(-1, 2, -3), B(5, 0, -6), C(0, 4, -1)$ are the vertices of a triangle $ABC$. The direction cosines of the internal bisector of $\angle BAC$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module