TS EAMCET · Maths · Three Dimensional Geometry
The perpendicular distance from the point \(P(3,5,2)\) to the line \(L\) passing through the point \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}\) and parallel to the vector \(\hat{\mathbf{i}}+5 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) is
- A \(\frac{1}{\sqrt{6}}\)
- B \(\frac{2}{\sqrt{6}}\)
- C \(\frac{\sqrt{6}}{\sqrt{5}}\)
- D \(7 \sqrt{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{6}}\)
Step-by-step Solution
Detailed explanation
Line passing through \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}\) and parallel to \(\hat{\mathbf{i}}+5 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) is \( \frac{x-2}{1}=\frac{y-1}{5}=\frac{z}{2}=t \) (Let) Any point taken on the given straight line will be \(P=(t+2,5 t+1,2 t)\) Let \(P\) is…
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