Find the Cartesian equation of the plane \vec{r}.(2\hat{i}+\hat{j}-\hat{k})=4.

(a) x+y-z=-4

(b) 2x+y-z=4

(c) x+y+z=4

(d) -2x-y+z=4

I have been asked this question in an international level competition.

The origin of the question is Three Dimensional Geometry topic in division Three Dimensional Geometry of Mathematics – Class 12

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

Correct option is (b) 2x+y-z=4

The best explanation: Given that the equation of the plane is \vec{r}.(2\hat{i}+\hat{j}-\hat{k})=4

We know that, \vec{r}=x\hat{i}+y\hat{j}+z\hat{k}

∴(x\hat{i}+y\hat{j}+z\hat{k}).(2\hat{i}+\hat{j}-\hat{k})=4

⇒2x+y-z=4 is the Cartesian equation of the plane.