TS EAMCET 2018 (04-May Shift-1)

The position vectors of the points $P$ and $Q$ are respectively $-2\overline{i}-3\overline{j}+\overline{k}$ and $3\overline{i}+3\overline{j}+2\overline{k}.$ The ratio in which the point having position vector $\frac{-9}{2}\overline{i}-6\overline{j}+\frac{1}{2}\overline{k}$ divides the line segment joining $P$ and $Q$ is

The centroid of a triangle with vertices $A(3, 4, 5), B(6, 7, 2)$ and $C(x, y, z)$ is $(3, 2, 3)$ then $x+y+z=$

The perpendicular distance from the origin to the plane containing the points having position vectors $\hat{i}+2\hat{j}+3\hat{k}, 2\hat{i}+3\hat{j}-4\hat{k}, 3\hat{i}-4\hat{j}+5\hat{k}$ is

A point on the plane determined by the points $A(1, 1, -1), B(2, -1, 0)$ and $C(-1, 0, 2)$ among the following is

The Cartesian equation of a plane parallel to the plane $\overrightarrow{r}·(2\hat{i}+3\hat{j}-4\hat{k})=1$ and at a distance of $2$ units from it is

Suppose $L_1$ and $L_2$ are two lines having the direction ratios $1,-2,-2$ and $0, 2, 1$ respectively. If the direction cosines of a line perpendicular to both $L_1$ and $L_2$ are $l, m, n$ then $\left|l\right|+\left|m\right|+|n\mid =$

The shortest distance between the Skew lines $\overrightarrow{r}=(3\hat{i}+4\hat{j}-2\hat{k})+\lambda (-\hat{i}+2\hat{j}+\hat{k})$ and $\overrightarrow{r}=(\hat{i}-7\hat{j}-2\hat{k})+\mu (\hat{i}+3\hat{j}+2\hat{k})$ is

If $(2, -1, 2)$ and $(K, -3, -5)$ are the triads of direction ratios of two lines and the angle between the lines is $60°,$ then