TS EAMCET · Maths · Three Dimensional Geometry
If \(\alpha\) and \(\beta\) are scalar and \(\mathbf{r}=(2+\alpha-3 \beta) \hat{\mathbf{i}}+(\beta-3) \hat{\mathbf{j}}+(2 \alpha-5 \beta-1) \hat{\mathbf{k}}\) is equation of a plane, then that equation in Cartesian form is
- A \(2 x+y-z+2=0\)
- B \(2 x-y-z=8\)
- C \(2 x-y-z+8=0\)
- D \(2 x+y-z=2\)
Answer & Solution
Correct Answer
(D) \(2 x+y-z=2\)
Step-by-step Solution
Detailed explanation
\(\mathbf{r}=(2+\alpha-3 \beta) \hat{\mathbf{i}}+(\beta-3) \hat{\mathbf{j}}+(2 \alpha-5 \beta-1) \hat{\mathbf{k}}\) Let \(\quad \mathbf{r}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}\) From Eq. (i), we get…
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