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

Vedclass · Accepted Answer

$(-8, 17, 3)$

Vedclass · Answer

(A) The coordinates of point $R$ that divides the line segment joining points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ externally in the ratio $m:n$ are given by the 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: $x = \frac{2(1) - 3(-2)}{2-3} = \frac{2 + 6}{-1} = -8$ $y = \frac{2(-4) - 3(3)}{2-3} = \frac{-8 - 9}{-1} = \frac{-17}{-1} = 17$ $z = \frac{2(6) - 3(5)}{2-3} = \frac{12 - 15}{-1} = \frac{-3}{-1} = 3$ Thus,the coordinates of the required point are $(-8, 17, 3)$.

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.

Similar Questions

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

The $x-$coordinate of a point on the line joining the points $Q(2, 2, 1)$ and $R(5, 1, -2)$ is $4$. Find its $z-$coordinate.

If the point dividing internally the line segment joining the points $(a, b)$ and $(5, 7)$ in the ratio $2 : 1$ is $(4, 6)$,then

$XOZ$-plane divides the line segment joining the points $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio: (in $: 7$)

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