Question

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

Answer 1

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.