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 $P(x, y, z)$ be the point which divides the line segment joining $A(1, -2, 3)$ and $B(3, 4, -5)$ internally in the ratio $m:n = 2:3$. Using th

Vedclass · Accepted Answer

$\left(\frac{9}{5}, \frac{2}{5}, -\frac{1}{5}\right)$

Vedclass · Answer

(A) Let $P(x, y, z)$ be the point which divides the line segment joining $A(1, -2, 3)$ and $B(3, 4, -5)$ internally in the ratio $m:n = 2:3$. Using the section formula: $x = \frac{mx_2 + nx_1}{m+n} = \frac{2(3) + 3(1)}{2+3} = \frac{6+3}{5} = \frac{9}{5}$ $y = \frac{my_2 + ny_1}{m+n} = \frac{2(4) + 3(-2)}{2+3} = \frac{8-6}{5} = \frac{2}{5}$ $z = \frac{mz_2 + nz_1}{m+n} = \frac{2(-5) + 3(3)}{2+3} = \frac{-10+9}{5} = -\frac{1}{5}$ Thus,the required point is $\left(\frac{9}{5}, \frac{2}{5}, -\frac{1}{5}\right)$.

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

Similar Questions

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

If $m:n$ is the ratio in which the point $\left(\frac{8}{5}, -\frac{1}{5}, \frac{8}{5}\right)$ divides the line segment joining the points $(2, p, 2)$ and $(p, -2, p)$, where $p$ is an integer, then $\frac{3m+n}{3n} =$

If the centroid of a tetrahedron $OABC$ is $(1, 2, -1)$, where $O$ is the origin, $A(a, 2, 3)$, $B(1, b, 2)$, and $C(2, 1, c)$ are the other vertices, then the distance of the point $P(a, b, c)$ from the origin is...

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 $A(4,7,8)$, $B(2,3,4)$, and $C(2,5,7)$ are the vertices of $\triangle ABC$, then the length of the internal bisector of the angle $A$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module