The point dividing the line segment joining ( | vedclass

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

Question

(B) Let the required point be $P(x, y, z)$. By the section formula,the coordinates of point $P$ dividing the line segment joining $(x_1, y_1, z_1)$ an

Vedclass · Accepted Answer

$(1, 0, 5)$

Vedclass · Answer

(B) Let the required point be $P(x, y, z)$. By the section formula,the coordinates of point $P$ dividing the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in the ratio $m:n$ are given by:$P = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n}\right)$Here,$(x_1, y_1, z_1) = (3, -2, 1)$,$(x_2, y_2, z_2) = (-2, 3, 11)$,$m = 2$,and $n = 3$.Substituting these values into the formula:$P = \left(\frac{2(-2) + 3(3)}{2+3}, \frac{2(3) + 3(-2)}{2+3}, \frac{2(11) + 3(1)}{2+3}\right)$$P = \left(\frac{-4 + 9}{5}, \frac{6 - 6}{5}, \frac{22 + 3}{5}\right)$$P = \left(\frac{5}{5}, \frac{0}{5}, \frac{25}{5}\right)$$P = (1, 0, 5)$

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

Similar Questions

If $A(4,3,5)$,$B(0,-2,2)$,and $C(3,2,1)$ are three points,then the coordinates of the point $D$ where the bisector of $\angle BAC$ meets the side $BC$ are:

$A$ point $P(5, -1)$ divides the line segment joining points $A(11, -3)$ and $B(x, y)$ in the ratio $2:3$. Find the coordinates of point $B$.

The points $(a, b)$,$(c, d)$,and $\left( \frac{kc + la}{k + l}, \frac{kd + lb}{k + l} \right)$ are:

If $P$ divides the line segment joining the points $A(1, 2, -1)$ and $B(-1, 0, 1)$ externally in the ratio $1: 2$ and $Q = (1, 3, -1)$,then $PQ =$

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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module