Embibe Experts Solutions for Chapter: Three Dimensional Geometry, Exercise 1: MHT-CET 2017

If a line in octant $OXYZ$ makes equal angles with co-ordinate axes, then

If a line makes angles ${120}^o$ and ${60}^o$ with the positive directions of $X$ and $Z$ axes respectively then the angle made by the line with positive $Y-$ axis is

If points $P\left(4, 5, x\right), Q\left(3, y, 4\right)$ and $R\left(5, 8, 0\right)$ are collinear, then the value of $x+y$ is

If vector $\overrightarrow{r}$ with direction cosine $l,m,n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is

$∆ABC$ has vertices at $A\equiv \left(2, 3, 5\right), B\equiv (-1, 3, 2)$ and $C\equiv \left(\lambda , 5, \mu \right).$ If the median through $A$ is equally inclined to the axes, then the values of $\lambda$ and $\mu$ respectively are