Equation of a Plane Passing through a Point and Perpendicular to a Given Vector

Q.

Equation of plane passing through a point A given by position vector $\overline{a}$ and perpendicular to $\hat{n}is(\overline{r}-\overline{a}).\hat{n}=0$ .

1. True

2. False

Q.

Equation of plane passing through points given by position vectors $\overline{a}and\overline{b}$ and origin will be

1. $\overline{r}.\frac{\overline{a}-\overline{b}}{|\overline{a}\times \overline{b}|}=0.$

2. $\overline{r}.\frac{\overline{a}+\overline{b}}{|\overline{a}\times \overline{b}|}=0.$

3. $\overline{r}.\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}=0.$

4. $\overline{r}.\left(\frac{\overline{a}.\overline{b}}{|\overline{a}\times \overline{b}|}\right)=0.$

Q. The vector equation of a plane which is at a distance of 9 units from the origin and which is normal to the
vector $2\hat{i}-\hat{j}+2\hat{k}$ is

1. $\overrightarrow{r}.(2\hat{i}-\hat{j}+2\hat{k})=27$
2. $\overrightarrow{r.}(2\hat{i}-\hat{j}+2\hat{k})=9$
3. $\overrightarrow{r}.(2\hat{i}-\hat{j}+2\hat{k})=3$

Q.

Equation of plane passing through a point A given by position vector $\overline{a}$ and perpendicular to $\hat{n}is(\overline{r}-\overline{a}).\hat{n}=0$ .

1. True

2. False

Q.

Equation of plane passing through points given by position vectors $\overline{a}and\overline{b}$ and origin will be

1. $\overline{r}.\frac{\overline{a}-\overline{b}}{|\overline{a}\times \overline{b}|}=0.$

2. $\overline{r}.\frac{\overline{a}+\overline{b}}{|\overline{a}\times \overline{b}|}=0.$

3. $\overline{r}.\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}=0.$

4. $\overline{r}.\left(\frac{\overline{a}.\overline{b}}{|\overline{a}\times \overline{b}|}\right)=0.$