The ratio in which the yz-plane divides the l | vedclass

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

Question

(A) The equation of the $yz$-plane is $x = 0$. Let the ratio in which the $yz$-plane divides the line segment joining $A(-3, 4, -2)$ and $B(2, 1, 3)$

Vedclass · Accepted Answer

$3: 2$

Vedclass · Answer

(A) The equation of the $yz$-plane is $x = 0$. Let the ratio in which the $yz$-plane divides the line segment joining $A(-3, 4, -2)$ and $B(2, 1, 3)$ be $k: 1$. Using the section formula, the coordinates of the point dividing the segment are: $P = \left( \frac{k(2) + 1(-3)}{k+1}, \frac{k(1) + 1(4)}{k+1}, \frac{k(3) + 1(-2)}{k+1} \right)$. Since the point $P$ lies on the $yz$-plane, its $x$-coordinate must be $0$: $\frac{2k - 3}{k+1} = 0$. $2k - 3 = 0 \implies 2k = 3 \implies k = \frac{3}{2}$. Thus, the ratio is $k: 1 = \frac{3}{2}: 1 = 3: 2$.

The ratio in which the $yz$-plane divides the line segment joining $(-3, 4, -2)$ and $(2, 1, 3)$ is

Similar Questions

Find the coordinates of the point which divides the line segment joining the points $(-2, 3, 5)$ and $(1, -4, 6)$ in the ratio $2:3$ externally.

The harmonic conjugate of $(2,3,4)$ with respect to the points $(3,-2,2)$ and $(6,-17,-4)$ is

The harmonic conjugate of the point $P(2,3,4)$ with respect to the points $A(3,-2,2)$ and $B(6,-17,-4)$ 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 $CD=$

Points $A(3, 2, 4)$, $B\left(\frac{33}{5}, \frac{28}{5}, \frac{38}{5}\right)$ and $C(9, 8, 10)$ are given. The ratio in which $B$ divides $\overline{AC}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module