Embibe Experts Solutions for Chapter: Three Dimensional Geometry, Exercise 1: Assam CEE 2018

If a variable plane forms a tetrahedron of constant volume $64k^3$ with the co-ordinate planes, then the locus of the centroid of the tetrahedron is:

The equation $(x-1)(x-2)=0$ represents, in three dimensional space, a:

The lines $\overline{r}={\overline{a}}_1+t{\overline{v}}_1$ and $\overline{r}={\overline{a}}_2+s{\overline{v}}_2,$ lie in a plane $\left({\overline{v}}_1\times {\overline{v}}_2\ne \overline{0}\right)$ if:

The ratio in which the plane $\overrightarrow{r}\left(\hat{\mathrm{i}}-2\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)=17$ divides the line joining the points $-2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+7\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}}-5\hat{\mathrm{j}}+8\hat{\mathrm{k}}$ is

The number of straight lines that are equally inclined to the three-dimensional coordinate axes is

The value of $\lambda$ for which the straight line $\frac{x-1}{1+\lambda }=\frac{y+1}{1-\lambda }=\frac{z-5}{-4}$ may lie on the plane $2x-3y+z=0$ is

İn three-dimensional space $x^2+x-12=0$ represents

The graph of the equation $x^2+y^2=0$ in three-dimensional space is