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 co

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

Find the coordinates of the points which trisect the line segment joining the points $A(2, 1, -3)$ and $B(5, -8, 3)$.

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 $\angle A$.

The coordinates of the point which divides the line segment joining the points $(2, -1, 3)$ and $(4, 3, 1)$ in the ratio $3 : 4$ internally are given by:

The point dividing the line segment joining $(3, -2, 1)$ and $(-2, 3, 11)$ in the ratio $2:3$ is

The point dividing the line segment joining the points $(1, 2, 3)$ and $(3, -5, 6)$ in the ratio $3: -5$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module