A) \[\mathbf{r}.(2\mathbf{i}+\mathbf{j}+\mathbf{k})=24\]
B) \[\mathbf{r}.(2\mathbf{i}+\mathbf{j}+2\mathbf{k})=24\]
C) \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=24\]
D) None of these
Correct Answer: B
Solution :
Here \[d=8\] and \[\mathbf{n}=2\mathbf{i}+\mathbf{j}+2\mathbf{k})\] \ \[\mathbf{\hat{n}}=\frac{\mathbf{n}}{|\mathbf{n}|}=\frac{2\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{4+1+4}}=\frac{2}{3}\mathbf{i}+\frac{1}{3}\mathbf{j}+\frac{2}{3}\mathbf{k}\] Hence, the required equation of the plane is \[\mathbf{r}.\left( \frac{2}{3}\mathbf{i}+\frac{1}{3}\mathbf{j}+\frac{2}{3}\mathbf{k} \right)=8\] or \[\mathbf{r}.(2\mathbf{i}+\mathbf{j}+2\mathbf{k})=24\].
You need to login to perform this action.
You will be redirected in
3 sec
