Question

The position vectors of two points P and Q are $3\mathbf{i} + \mathbf{j} + 2\mathbf{k}$ and $\mathbf{i} - 2\mathbf{j} - 4\mathbf{k}$ respectively. The equation of the plane through Q and perpendicular to PQ is

• A. $\mathbf{r}.(2\mathbf{i} + 3\mathbf{j} + 6\mathbf{k}) = 28$
• B. $\mathbf{r}.(2\mathbf{i} + 3\mathbf{j} + 6\mathbf{k}) = 32$
• C. $\mathbf{r}.(2\mathbf{i} + 3\mathbf{j} + 6\mathbf{k}) + 28 = 0$
• D. None of these

Answer 1

Answer: (C)

$\mathbf{r}.(2\mathbf{i} + 3\mathbf{j} + 6\mathbf{k}) + 28 = 0$

Answer 2

The required plane is $\{\mathbf{r} - (\mathbf{i} - 2\mathbf{j} - 4\mathbf{k})\}.\overset{\rightarrow}{PQ} = 0$.