Embibe Experts Solutions for Exercise 1: Assignment

Find the ratio in which the plane $x+2y-3z=2$ divides the join of $A\left(3,1,3\right)$ and $B\left(-1,2,1\right)$. Find the coordinates of the point of intersection of the line and the plane.

The points $A\left(3,2,0\right),B\left(5,3,2\right)$ and $C\left(0,2,4\right)$ are the vertices of a triangle. Find the distance of the point $A$ from the point in which bisector of angle $\angle BAC$ meets $BC$.

Prove the points $A\left(3,2,-4\right),B\left(9,8,-10\right)$ and $C\left(5,4,-6\right)$ are collinear. Also, find the ratio in which $C$ divides $AB$.

Find the locus of a point $P$ which moves in such a way that $3AP=4PB$, where $A\left(1,-2,3\right)$ and $B\left(1,2,3\right)$ are the given points.

Find the locus of a point $P$ such that $3P{A}^2=2P{B}^2$,  where $A\left(1,1,4\right)$ and $B\left(2,1,3\right)$ are given points.

Find the ratio in which the line segment joining the points $\left(4,8,10\right)$ and $\left(6,10,10\right)$ is divided by $XZ$-plane. Also, find the coordinates of the point of intersection of the line and the plane.

Find the lengths of medians of the triangle with vertices $\left(1,2,3\right),\left(-2,5,6\right)$ and $\left(2,-1,3\right)$.

Find the locus of a point equidistant from points $\left(1,2,3\right)$ and $\left(3,4,5\right)$