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

Category: QuestionsFind the Cartesian equation of the plane \vec{r}.(2\hat{i}+\hat{j}-\hat{k})=4.
Editor">Editor Staff asked 11 months ago

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 
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1 Answers
Editor">Editor Staff answered 11 months ago

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.