The coordinates of the point where the line j | vedclass

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

Question

(A) The equation of the $yz$-plane is $x = 0$. Let the point $P$ divide the line segment joining $A(3, 5, -7)$ and $B(-2, 1, 8)$ in the ratio $k:1$. T

Vedclass · Accepted Answer

$\left(0, \frac{13}{5}, 2\right)$

Vedclass · Answer

(A) The equation of the $yz$-plane is $x = 0$. Let the point $P$ divide the line segment joining $A(3, 5, -7)$ and $B(-2, 1, 8)$ in the ratio $k:1$. The coordinates of $P$ are given by $\left(\frac{-2k + 3}{k+1}, \frac{k + 5}{k+1}, \frac{8k - 7}{k+1}\right)$. Since $P$ lies on the $yz$-plane,its $x$-coordinate must be $0$: $\frac{-2k + 3}{k+1} = 0 \implies -2k + 3 = 0 \implies k = \frac{3}{2}$. Substituting $k = \frac{3}{2}$ into the coordinates of $P$: $y = \frac{\frac{3}{2} + 5}{\frac{3}{2} + 1} = \frac{\frac{13}{2}}{\frac{5}{2}} = \frac{13}{5}$. $z = \frac{8(\frac{3}{2}) - 7}{\frac{3}{2} + 1} = \frac{12 - 7}{\frac{5}{2}} = \frac{5}{\frac{5}{2}} = 2$. Thus,the coordinates are $\left(0, \frac{13}{5}, 2\right)$.

The coordinates of the point where the line joining the points $(3, 5, -7)$ and $(-2, 1, 8)$ is intersected by the $yz$-plane are given by:

Similar Questions

If $A(1,1,2)$, $B(4,2,1)$ and $C(2,3,5)$ are the vertices of a triangle, then a vector representing the median of the triangle through $A$ is

The coordinates of the points on the line $\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}$ at a distance of $12 \text{ units}$ from the point $A(-2, 1, -1)$ are

The coordinates of the point where the line passing through $P(3, 4, 1)$ and $Q(5, 1, 6)$ crosses the $xy$-plane are:

If the two lines $\frac{x - 1}{2} = \frac{y - 1}{3} = \frac{z - 1}{4}$ and $\frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}$ intersect at a point,then find the value of $k$.

If the shortest distance between the lines $\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}$ and $\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}$ is $\frac{6}{\sqrt{5}}$,then the sum of all possible values of $\lambda$ is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module