The ratio in which the line joining the point | vedclass

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

Question

(C) Let the ratio in which the $yz$-plane divides the line segment joining the points $A(2, 4, 5)$ and $B(3, 5, -4)$ be $k:1$.By the section formula,t

Vedclass · Accepted Answer

$-2:3$

Vedclass · Answer

(C) Let the ratio in which the $yz$-plane divides the line segment joining the points $A(2, 4, 5)$ and $B(3, 5, -4)$ be $k:1$.By the section formula,the coordinates of the point dividing the segment are given by $\left( \frac{3k+2}{k+1}, \frac{5k+4}{k+1}, \frac{-4k+5}{k+1} \right)$.Since the point lies on the $yz$-plane,its $x$-coordinate must be zero.Therefore,$\frac{3k+2}{k+1} = 0$.This implies $3k + 2 = 0$,so $k = -\frac{2}{3}$.Thus,the ratio is $-\frac{2}{3}:1$,which is $-2:3$.

The ratio in which the line joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is divided by the $yz$-plane is

Similar Questions

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

Let $A(4,3,5), B(1,-2,1), C(3,2,1)$ be the vertices of a triangle $ABC$. If the internal bisector of $\angle BAC$ meets the side $BC$ at $D$, then $CD=$

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:

Using the section formula,prove that the three points $A(-4, 6, 10)$,$B(2, 4, 6)$,and $C(14, 0, -2)$ are collinear.

Vedclass Test Series

Exam Paper Generator

Online Exam Module