Embibe Experts Solutions for Chapter: Three Dimensional Geometry, Exercise 1: GUJCET 2017

The position vector of point $A$ is $(4,2,-3).$ If $p_1$ is perpendicular distance of $A$ from $XY$ -plane and $p_2$ is perpendicular distance from $Y$-axis, then $p_1+p_2=$ _______.

The direction angles of the line $x=4z+3, y=2-3z$ are $\alpha , \beta$ and $\gamma ,$ then $\cos \alpha +\cos \beta +\cos \gamma =$ _______.

Lines $\overrightarrow{r}=\left(3+t\right)\hat{i}+\left(1-t\right)\hat{j}+\left(-2-2t\right)\hat{k}, t\in R$ and $x=4+k, y=-k, z=-4-2k, k\in R,$ then relation between lines is

Plane $ax+by+cz=1$ intersect axes in $A, B, C$ respectively. If $G\left(\frac{1}{6},-\frac{1}{3},1\right)$ is the centroid of $\Delta ABC,$ then $a+b+3c=$_______.

If the normal of the plane makes an angles $\frac{\pi }{4},\frac{\pi }{4}$ and $\frac{\pi }{2}$ with positive $X$-axis, $Y$-axis and $Z$-axis respectively and the length of the perpendicular line segment from origin to the plane is $\sqrt{2},$ then the equation of the plane is ______.

If a plane has $X$-intercept $l, Y$-intercept $m$ and $Z-$intercept $n,$ and perpendicular distance of plane from origin is $k,$ then

The equation of plane containing intersecting lines $\frac{x+3}{3}=\frac{y}{1}=\frac{z-2}{2}$ and $\frac{x-3}{4}=\frac{y-2}{2}=\frac{z-6}{3}$ is