MHT CET · Maths · Three Dimensional Geometry
The distance of the plane \(\overline{\mathrm{r}}=(\hat{i}-\hat{\mathrm{j}})+\lambda(\hat{i}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\mu(\hat{i}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})\) from the origin is
- A \(\frac{7}{\sqrt{38}}\) units
- B \(\frac{1}{\sqrt{38}}\) units
- C \(\frac{5}{\sqrt{38}}\) units
- D \(\frac{2}{\sqrt{38}}\) units
Answer & Solution
Correct Answer
(A) \(\frac{7}{\sqrt{38}}\) units
Step-by-step Solution
Detailed explanation
\(\overline{\mathrm{n}} = (\hat{i}+\hat{\mathrm{j}}+\hat{\mathrm{k}}) \times (\hat{i}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})\) \(\overline{\mathrm{n}} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 1 & -2 & 3 \end{vmatrix} = \hat{i}(3+2)-\hat{j}(3-1)+\hat{k}(-2-1)\)
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