JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(P\) be the point \((10,-2,-1)\) and \(Q\) be the foot of the perpendicular drawn from the point \(\mathrm{R}(1,7,6)\) on the line passing through the points \((2,-5,11)\) and \((-6,7,-5)\). Then the length of the line segment \(\mathrm{PQ}\) is equal to ..........
- A \(13\)
- B \(18\)
- C \(34\)
- D \(67\)
Answer & Solution
Correct Answer
(A) \(13\)
Step-by-step Solution
Detailed explanation
\( \text { Line }: \frac{x+6}{-8}=\frac{y-7}{12}=\frac{z+5}{-16} \) \( \frac{x+6}{2}=\frac{y-7}{-3}=\frac{z+5}{4}=\lambda \) \( Q(2 \lambda-6,7-3 \lambda, 4 \lambda-5) \) \( \overline{Q R}(2 \lambda-7,-3 \lambda, 4 \lambda-11) \)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The number of solutions of the equation \(\log _{(x+1)}\left(2 x^{2}+7 x+5\right)+\log _{(2 x+5)}(x+1)^{2}-4=0, x\,>\,0\), is \(....\)JEE Mains 2021 Hard
- The mean and variance of \(n\) observations are \(8\) and \(16\), respectively. If the sum of the first \((n-1)\) observations is \(48\) and the sum of squares of the first \((n-1)\) observations is \(496\), then the value of \(n\) is:JEE Mains 2026 Medium
- Consider the set of all lines \(px + qy + r = 0\) such that \(3p + 2q + 4r = 0\) . Which one of the following statements is true?JEE Mains 2019 Hard
- Let \(\overrightarrow{\mathrm{a}}=\hat{i}+2 \hat{j}+\hat{k}\) and \(\quad \overrightarrow{\mathrm{b}}=2 \hat{i}+7 \hat{j}+3 \hat{k} . \quad\) Let \(\mathrm{L}_1: \overrightarrow{\mathrm{r}}=(-\hat{i}+2 \hat{j}+\hat{k})+\lambda \overrightarrow{\mathrm{a}}, \lambda \in \mathbf{R}\) and \(\mathrm{L}_2: \overrightarrow{\mathrm{r}}=(\hat{j}+\hat{k})+\mu \overrightarrow{\mathrm{b}}, \mu \in \mathbf{R}\) be two lines. If the line \(\mathrm{L}_3\) passes through the point of intersection of \(\mathrm{L}_1\) and \(L_2\), and is parallel to \(\vec{a}+\vec{b}\), then \(L_3\) passes through the point :JEE Mains 2025 Medium
- Let the area enclosed by the lines \(x + y =2, y =0\), \(x=0\) and the curve \(f(x)=\min \left\{x^2+\frac{3}{4}, 1+[x]\right\}\) where \([ x ]\) denotes the greatest integer \(\leq x\), be \(A\). Then the value of \(12\,A\) is \(............\).JEE Mains 2023 Hard
- Let \(A B C\) be an isosceles triangle in which \(A\) is at \((-1,0), \angle A=\frac{2 \pi}{3}, A B=A C\) and \(B\) is on the positive \(\mathrm{x}\)-axis. If \(\mathrm{BC}=4 \sqrt{3}\) and the line \(\mathrm{BC}\) intersects the line \(y=x+3\) at \((\alpha, \beta)\), then \(\frac{\beta^4}{\alpha^2}\) is :JEE Mains 2024 Hard
More PYQs from JEE Mains
- If a circle of radius \(R\) passes through the origin \(O\) and intersects the coordinate axes at \(A\) and \(B,\) then the locus of the foot of perpendicular from \(O\) on \(AB\) isJEE Mains 2019 Hard
- Two tangents are drawn from the point \(\mathrm{P}(-1,1)\) to the circle \(\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-6 \mathrm{y}+6=0\). If these tangents touch the circle at points \(A\) and \(B\), and if \(D\) is a point on the circle such that length of the segments \(A B\) and \(A D\) are equal, then the area of the triangle \(A B D\) is eqaul to:JEE Mains 2021 Medium
- If the lines \(\frac{{x - 2}}{1} = \frac{{y - 3}}{1} = \frac{{z - 4}}{{ - k}}\) and \(\frac{{x - 1}}{k} = \frac{{y - 4}}{2} = \frac{{z - 5}}{1}\) are coplanar then \(k \) can haveJEE Mains 2013 Easy
- If \(a_n=\frac{-2}{4 n^2-16 n+15}\), then \(a_1+a_2+\ldots \ldots+a_{25}\) is equal to :JEE Mains 2023 Hard
- The tangent at the point \((2, -2)\) to the curve, \(x^2y^2 - 2x = 4\, (1 -y)\) does not pass through the pointJEE Mains 2017 Hard
- Let \(p,q\in R.\) if \(2-\sqrt 3\) is a root of the quadratic equation, \(x^2 + px + q = 0,\) thenJEE Mains 2019 Hard