Condition for a Line to Lie in a Plane

Q. The plane containing the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z-1}{3}$ and also containing its projection on the plane $2x+3y-z=5$, contains which one of the following points ?

1. $(2,2,0)$
2. $(0,-2,2)$
3. $(2,0,-2)$
4. $(-2,2,2)$

Q. The intercept made by the plane $\overrightarrow{r}.\overrightarrow{n}=q$ on the x-axis is

1. $(\hat{i}.\overrightarrow{n})q$
2. $\frac{q}{\left|\overrightarrow{n}\right|}$
3. $\frac{q}{\hat{i}.\overrightarrow{n}}$
4. $\frac{\hat{i}.\overrightarrow{n}}{q}$

Q. $ABCD$ is a tetrahedron and $O$ is any point. If the line joining $O$ to the vertices meets the opposite faces at $P,Q,R$ and $S$, then the value of
$\frac{OP}{AP}+\frac{OQ}{BQ}+\frac{OR}{CR}+\frac{OS}{DS}$ is

Q. The feasible region of an LPP is shown in the figure.
If $Z=5x+2y,$ then the maximum value of $Z$ occurs at

$\left(a\right)(0,0)\left(b\right)(5,0)$
$\left(c\right)(2,4)\left(d\right)(0,4)$

Q. The intercept made by the plane $\overrightarrow{r}.\overrightarrow{n}=q$ on the x-axis is

1. $\frac{q}{\hat{i}.\overrightarrow{n}}$
2. $\frac{\hat{i}.\overrightarrow{n}}{q}$
3. $(\hat{i}.\overrightarrow{n})q$
4. $\frac{q}{\left|\overrightarrow{n}\right|}$

Q. The feasible region of an LPP is shown in the figure. If $z=3x+9y$, then the minimum value of $z$ occurs at

1. $(5,5)$
2. $(0,10)$
3. $(0,20)$
4. $(15,15)$

Q. The plane containing the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z-1}{3}$ and also containing its projection on the plane $2x+3y-z=5$, contains which one of the following points ?

1. $(0,-2,2)$
2. $(2,0,-2)$
3. $(2,2,0)$
4. $(-2,2,2)$

Q. The intercept made by the plane $\overrightarrow{r}.\overrightarrow{n}=q$ on the x-axis is

1. $\frac{q}{\hat{i}.\overrightarrow{n}}$
2. $\frac{\hat{i}.\overrightarrow{n}}{q}$
3. $(\hat{i}.\overrightarrow{n})q$
4. $\frac{q}{\left|\overrightarrow{n}\right|}$