The ratio in which Bleft(frac{33}{5}, frac{28 | vedclass

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

Question

(C) Let the point $B$ divide the line segment $AC$ in the ratio $k: 1$. Using the section formula, the coordinates of $B$ are given by: $B = \left( \f

Vedclass · Accepted Answer

$3: 2$

Vedclass · Answer

(C) Let the point $B$ divide the line segment $AC$ in the ratio $k: 1$. Using the section formula, the coordinates of $B$ are given by: $B = \left( \frac{k(9) + 1(3)}{k+1}, \frac{k(8) + 1(2)}{k+1}, \frac{k(10) + 1(4)}{k+1} \right)$ Given that $B = \left( \frac{33}{5}, \frac{28}{5}, \frac{38}{5} \right)$, we equate the $x$-coordinates: $\frac{9k + 3}{k + 1} = \frac{33}{5}$ $5(9k + 3) = 33(k + 1)$ $45k + 15 = 33k + 33$ $45k - 33k = 33 - 15$ $12k = 18$ $k = \frac{18}{12} = \frac{3}{2}$ Thus, the ratio $k: 1$ is $3: 2$.

The ratio in which $B\left(\frac{33}{5}, \frac{28}{5}, \frac{38}{5}\right)$ divides the line segment joining $A(3, 2, 4)$ and $C(9, 8, 10)$ is

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 harmonic conjugate of $P(-9, 12, -15)$ with respect to the line segment $AB$,where $A=(1, -2, 3)$ and $B=(-4, 5, -6)$ is

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

The harmonic conjugate of the point $P(2,3,4)$ with respect to the points $A(3,-2,2)$ and $B(6,-17,-4)$ is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module