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) The coordinates of a point $R$ that divides the line segment joining points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ internally in the ratio $m:n

Vedclass · Accepted Answer

$\left(-\frac{4}{5}, \frac{1}{5}, \frac{27}{5}\right)$

Vedclass · Answer

(A) The coordinates of a point $R$ that divides the line segment joining points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ internally in the ratio $m:n$ are given by the section formula:$\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n}\right)$Given points are $P(-2, 3, 5)$ and $Q(1, -4, 6)$ with ratio $m:n = 2:3$.Substituting the values:$x = \frac{2(1) + 3(-2)}{2+3} = \frac{2 - 6}{5} = -\frac{4}{5}$$y = \frac{2(-4) + 3(3)}{2+3} = \frac{-8 + 9}{5} = \frac{1}{5}$$z = \frac{2(6) + 3(5)}{2+3} = \frac{12 + 15}{5} = \frac{27}{5}$Thus,the coordinates of the required point are $\left(-\frac{4}{5}, \frac{1}{5}, \frac{27}{5}\right)$.

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

$O(0,0,0), A(3,1,4), B(1,3,2)$ and $C(0,4,-2)$ are the vertices of a tetrahedron. If $G$ is the centroid of the tetrahedron and $G_1$ is the centroid of its face $ABC$,then the point which divides $GG_1$ in the ratio $1:2$ 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 point dividing the line segment joining the points $(1, 2, 3)$ and $(3, -5, 6)$ in the ratio $3: -5$ is

The ratio in which the point $(5, -2)$ divides the line segment joining the points $(8, 4)$ and $(9, 6)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module