Find the Cartesian equation of the plane \(\vec{r}.[(λ+2μ) \hat{i}+(2λ-μ) \hat{j}+(3λ-2μ)\hat{k}]\)=12.

Category: QuestionsFind the Cartesian equation of the plane \(\vec{r}.[(λ+2μ) \hat{i}+(2λ-μ) \hat{j}+(3λ-2μ)\hat{k}]\)=12.
Editor">Editor Staff asked 11 months ago

Find the Cartesian equation of the plane \(\vec{r}.[(λ+2μ) \hat{i}+(2λ-μ) \hat{j}+(3λ-2μ)\hat{k}]\)=12.
 
(a) (λ-μ)x+y+(3λ-2μ)z=12
 
(b) (λ+3μ)x+(2+μ)y+(3λ-2μ)z=12
 
(c) (λ+2μ)x-2λy+(3λ-2μ)z=12
 
(d) (λ+2μ)x+(2λ-μ)y+(3λ-2μ)z=12
 
I have been asked this question during an online interview.
 
My question is based upon Three Dimensional Geometry in section 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 choice is (d) (λ+2μ)x+(2λ-μ)y+(3λ-2μ)z=12
 
Best explanation: Given that the equation of the plane is \vec{r}.[(λ+2μ) \hat{i}+(2λ-μ) \hat{j}+(3λ-2μ)\hat{k}]=12
 
We know that, \vec{r}=x\hat{i}+y\hat{j}+z\hat{k}
 
∴(x\hat{i}+y\hat{j}+z\hat{k}).([(λ+2μ) \hat{i}+(2λ-μ) \hat{j}+(3λ-2μ)\hat{k}])=12
 
⇒(λ+2μ)x+(2λ-μ)y+(3λ-2μ)z=12 is the Cartesian equation of the plane.