If z_1 and z_2 are the z-coordinates of the p | vedclass

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

Question

(D) The points of trisection divide the line segment $AB$ in the ratio $1:2$ and $2:1$ internally.Let the points be $P$ and $Q$ such that $P$ divides

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) The points of trisection divide the line segment $AB$ in the ratio $1:2$ and $2:1$ internally.Let the points be $P$ and $Q$ such that $P$ divides $AB$ in ratio $1:2$ and $Q$ divides $AB$ in ratio $2:1$.The $z$-coordinate of a point dividing the segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in ratio $m:n$ is given by $\frac{mz_2 + nz_1}{m+n}$.For $z_1$ (ratio $1:2$):$z_1 = \frac{1(6) + 2(4)}{1 + 2} = \frac{6 + 8}{3} = \frac{14}{3}$.For $z_2$ (ratio $2:1$):$z_2 = \frac{2(6) + 1(4)}{2 + 1} = \frac{12 + 4}{3} = \frac{16}{3}$.Therefore,$z_1 + z_2 = \frac{14}{3} + \frac{16}{3} = \frac{30}{3} = 10$.

If $z_1$ and $z_2$ are the $z$-coordinates of the points of trisection of the line segment joining the points $A(2, 1, 4)$ and $B(-1, 3, 6)$,then $z_1 + z_2 =$

Similar Questions

In what ratio does the $x$-axis divide the line segment joining the points $(3, 4)$ and $(5, 6)$?

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

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

The point dividing the join of $(3, -2, 1)$ and $(-2, 3, 11)$ in the ratio $2:3$ is

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module