Find the coordinates of the point which divid | vedclass

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

Question

(A) Let the points be $A(1, -2, 3)$ and $B(3, 4, -5)$. The point $P(x, y, z)$ divides the line segment $AB$ externally in the ratio $m:n = 2:3$.The se

Vedclass · Accepted Answer

$(-3, -14, 19)$

Vedclass · Answer

(A) Let the points be $A(1, -2, 3)$ and $B(3, 4, -5)$. The point $P(x, y, z)$ divides the line segment $AB$ externally in the ratio $m:n = 2:3$.The section formula for external division is given by:$x = \frac{mx_2 - nx_1}{m - n}, y = \frac{my_2 - ny_1}{m - n}, z = \frac{mz_2 - nz_1}{m - n}$Substituting the values $m=2, n=3, x_1=1, y_1=-2, z_1=3, x_2=3, y_2=4, z_2=-5$:$x = \frac{2(3) - 3(1)}{2 - 3} = \frac{6 - 3}{-1} = -3$$y = \frac{2(4) - 3(-2)}{2 - 3} = \frac{8 + 6}{-1} = -14$$z = \frac{2(-5) - 3(3)}{2 - 3} = \frac{-10 - 9}{-1} = 19$Thus,the coordinates of the point are $(-3, -14, 19)$.

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

Similar Questions

If $A (1, 2, -1)$ and $B (-1, 0, 1)$ are two points,then the coordinates of the point which divides $AB$ externally in the ratio $1 : 2$ are:

If the line joining $A(1,3,4)$ and $B$ is divided by the point $P(-2,3,5)$ in the ratio $1:3$,then the coordinates of $B$ are:

The ratio in which $B\left(\frac{33}{5}, \frac{28}{5}, \frac{38}{5}\right)$ divides the line segment joining $A(3, 2, 4)$ and $C(9, 8, 10)$ is

If $A(1,2,3), B(2,-3,1), C(3,2,-1)$ are three vertices of a tetrahedron $ABCD$ and $G\left(\frac{5}{2}, \frac{3}{2}, \frac{9}{4}\right)$ is its centroid, then the point which divides $GD$ in the ratio $1:2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module