Embibe Experts Solutions for Chapter: Three Dimensional Geometry, Exercise 1: AP EAPCET - 20 Aug 2021 Forenoon

Let $O$ be the origin and $\text{'}P\text{'}$ be a point which is at a distance of $3$ units from the origin. If the direction ratios of $\overrightarrow{OP}$ are $(1,-2,-2)$, then the coordinates of $\text{'}P\text{'}$ are

Which of the following vector is equally inclined with the coordinate axes?

$A(-1,2,-3), B(5,0,-6), C(0,4,-1)$ are the vertices of a triangle $ABC$. The direction cosines of internal bisector of $\angle BAC$ are

The direction cosines of the line joining the points $(-2,4,-5)$ and $(1,2,3)$ are

The sum of intercepts of the plane $4 x+3 y+2 z=2$ on the coordinate axes is

$X$ intercept of the plane containing the line of intersection of the planes $x-2y+z+2=0$ and $3x-y-z+1=0$ and also passing through $(1,1,1)$ is

Find the equation of the plane passing through the point $(2,1,3)$ and perpendicular to the planes $x-2y+2z+3=0$ and $3x-2y+4z-4=0.$

Let $L_1$ (respectively $L_2$ ) be the line passing through $2\hat{i}-\hat{k}$ (respectively $2\hat{i}+\hat{j}-3\hat{k}$) and parallel to $3\hat{i}-\hat{j}+2\hat{k}$ (respectively $\hat{i}-2\hat{j}+\hat{k}$). Then the shortest distance between the lines $L_1$ and $L_2$ is equal to