XOZ-plane divides the line segment joining th | vedclass

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

Question

(C) Let the $XOZ$-plane divide the line segment joining the points $A(2, 3, 1)$ and $B(6, 7, 1)$ in the ratio $m: n$. Using the section formula, the c

Vedclass · Accepted Answer

$-3$

Vedclass · Answer

(C) Let the $XOZ$-plane divide the line segment joining the points $A(2, 3, 1)$ and $B(6, 7, 1)$ in the ratio $m: n$. Using the section formula, the coordinates of the point of division are given by: $\left(\frac{m(6)+n(2)}{m+n}, \frac{m(7)+n(3)}{m+n}, \frac{m(1)+n(1)}{m+n}\right)$ Since the point lies on the $XOZ$-plane, its $y$-coordinate must be zero. Therefore, $\frac{7m + 3n}{m+n} = 0$. $7m + 3n = 0$ $7m = -3n$ $\frac{m}{n} = -\frac{3}{7}$ Thus, the ratio is $-3: 7$.

$XOZ$-plane divides the line segment joining the points $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio: (in $: 7$)

Similar Questions

Given that $P(3, 2, -4)$,$Q(5, 4, -6)$,and $R(9, 8, -10)$ are collinear. Find the ratio in which $Q$ divides $PR$.

If $A(4, 7, 8)$,$B(2, 3, 4)$,and $C(2, 5, 7)$ are the vertices of a triangle $ABC$,find the length of the angle bisector of $\angle A$.

Find the ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, -8)$ is divided by the $YZ$-plane.

If $P=(3,12,4)$ and $Q$ is a point on the line $OP$ such that $OQ=3$,then the sum of all the coordinates of $Q$ is

The harmonic conjugate of $P(-9, 12, -15)$ with respect to the line segment $AB$,where $A=(1, -2, 3)$ and $B=(-4, 5, -6)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module