Let A(3, 2, -4) and B(9, 8, -10) be two point | vedclass

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

Question

(B) The coordinates of $P_1$ dividing $AB$ in the ratio $1:2$ are given by the section formula:$P_1 = \left( \frac{1(9) + 2(3)}{1+2}, \frac{1(8) + 2(2

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The coordinates of $P_1$ dividing $AB$ in the ratio $1:2$ are given by the section formula:$P_1 = \left( \frac{1(9) + 2(3)}{1+2}, \frac{1(8) + 2(2)}{1+2}, \frac{1(-10) + 2(-4)}{1+2} \right) = \left( \frac{15}{3}, \frac{12}{3}, \frac{-18}{3} \right) = (5, 4, -6)$.The coordinates of $P_2$ dividing $AB$ in the ratio $2:1$ are:$P_2 = \left( \frac{2(9) + 1(3)}{2+1}, \frac{2(8) + 1(2)}{2+1}, \frac{2(-10) + 1(-4)}{2+1} \right) = \left( \frac{21}{3}, \frac{18}{3}, \frac{-24}{3} \right) = (7, 6, -8)$.Since $P(\alpha, \beta, \gamma)$ is the midpoint of $P_1 P_2$ (ratio $1:1$):$P = \left( \frac{5+7}{2}, \frac{4+6}{2}, \frac{-6-8}{2} \right) = (6, 5, -7)$.Thus, $\alpha = 6$, $\beta = 5$, and $\gamma = -7$.Calculating the expression:$\alpha + 2\beta + 2\gamma = 6 + 2(5) + 2(-7) = 6 + 10 - 14 = 2$.

Let $A(3, 2, -4)$ and $B(9, 8, -10)$ be two points. Let $P_1$ divide $AB$ in the ratio $1:2$ and $P_2$ divide $AB$ in the ratio $2:1$. If the point $P(\alpha, \beta, \gamma)$ divides $P_1 P_2$ in the ratio $1:1$, then $\alpha + 2\beta + 2\gamma =$

Similar Questions

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

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

Show that the points $A (1,-2,-8), B (5,0,-2)$ and $C (11,3,7)$ are collinear,and find the ratio in which $B$ divides $AC$.

Find the coordinates of the centroid of the triangle whose vertices are $(x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2})$ and $(x_{3}, y_{3}, z_{3})$.

If $A=(5,4,2), B=(6,2,-1), C=(8,-2,-7)$,then the harmonic conjugate of $A$ with respect to $B$ and $C$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module