JEE Mains · Maths · STD 12 - 11. three dimension geometry
The length of the perpendicular from the point \((2, -1, 4)\) on the straight line, \(\frac{{x + 3}}{{10}} = \frac{{y - 2}}{{ - 7}} = \frac{z}{1}\) is
- A greater than \(2\) but less than \(3\)
- B less than \(2\)
- C greater than \(4\)
- D greater than \(3\) but less than \(4\)
Answer & Solution
Correct Answer
(D) greater than \(3\) but less than \(4\)
Step-by-step Solution
Detailed explanation
Now, \(\overline{M P} \cdot(10 \hat{i}-7 \hat{j}+\hat{k})=0\) \(\Rightarrow \quad \lambda=\frac{1}{2}\) \(\therefore \) Length of perpendicular \((=P M)=\sqrt{0+\frac{1}{4}+\frac{49}{4}}\) \(=\sqrt{\frac{50}{4}}=\sqrt{\frac{25}{4}}=\frac{5}{\sqrt{2}}\) which is greater than 3…
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