AP EAMCET · Maths · Three Dimensional Geometry
The distance of a point \((2,3,-5)\) from the plane \(\vec{r} \cdot(4 \hat{i}-3 \hat{j}+2 \hat{k})=4\) is
- A \(\frac{11}{2}\)
- B \(\frac{11}{\sqrt{29}}\)
- C \(\frac{15}{\sqrt{29}}\)
- D \(\frac{11}{\sqrt{38}}\)
Answer & Solution
Correct Answer
(C) \(\frac{15}{\sqrt{29}}\)
Step-by-step Solution
Detailed explanation
Point \((2,3,-5)\), plane \(\vec{r} \cdot(4 \hat{i}-3 \hat{j}+2 \hat{k})=4\) Distance \(=\frac{|8-9-10-4|}{\sqrt{16+9+4}}=\frac{15}{\sqrt{29}}\).
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