AP EAMCET · Maths · Three Dimensional Geometry
The cartesian equation of the plane whose vector equation is \(\gamma=(1+\lambda-\mu) \hat{\mathbf{i}}+(2-\lambda) \hat{\mathbf{j}}+(3-2 \lambda+2 \mu) \hat{\mathbf{k}}\) where \(\lambda, \mu\) are scalars, is
- A \(2 x+y=5\)
- B \(2 x-y=5\)
- C \(2 x-z=5\)
- D \(2 x+z=5\)
Answer & Solution
Correct Answer
(D) \(2 x+z=5\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \gamma=(1+\lambda-\mu) \hat{i}+(2-\lambda) \hat{j}+(3-2 \lambda+2 \mu) \hat{k} \\ & =\hat{i}+\lambda \hat{i}-\mu \hat{i}+2 \hat{j}-\lambda \hat{j}+3 \hat{k}-2 \lambda \hat{k}+2 \mu \hat{k} \\ & =(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}-2…
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