JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(Q(a,b,c)\) be the image of the point \(P(3,2,1)\) in the line \(\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}.\) Then the distance of Q from the line \(\frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2}\) is
- A 6
- B 8
- C 7
- D 5
Answer & Solution
Correct Answer
(C) 7
Step-by-step Solution
Detailed explanation
drs of \(PN =< r -2,2 r -2, r >\) \(1 \cdot (r-2)+2(2 r-2)+1 \cdot (r)=0\) \(6 r=6 \Rightarrow r=1\) \(\therefore N \equiv(2,2,2)\) \(\Rightarrow Q \equiv(1,2,3)\) \(AQ =\sqrt{64+49+4}=\sqrt{117}\)…
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 foot of the perpendicular drawn from the point \((4,2,3)\) to the line joining the points \((1,-2,3)\) and \((1,1,0)\) lies on the planeJEE Mains 2020 Hard
- Let the eccentricity of the hyperbola \(H : \frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1\) be \(\sqrt{\frac{5}{2}}\) and length of its latus rectum be \(6 \sqrt{2}\), If \(y =2 x + c\) is a tangent to the hyperbola \(H\), then the value of \(c ^{2}\) is equal toJEE Mains 2022 Hard
- If the distance between the plane, \(23 \mathrm{x}-10 \mathrm{y}-2 \mathrm{z}+48=0\) and the plane containing the lines \(\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3}\) and \(\frac{x+3}{2}=\frac{y+2}{6}=\frac{z-1}{\lambda}(\lambda \in R)\) is equal to \(\frac{\mathrm{k}}{\sqrt{633}},\) then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- Let a unit vector \(\hat{ OP }\) make angle \(\alpha, \beta, \gamma\) with the positive directions of the co-ordinate axes \(OX , OY\), \(OZ\) respectively, where \(\beta \in\left(0, \frac{\pi}{2}\right) \hat{ OP }\) is perpendicular to the plane through points \((1,2,3)\), \((2,3,4)\) and \((1,5,7)\), then which one of the following is true ?JEE Mains 2023 Hard
- Let a function \(f: R \rightarrow R\) be defined as :
\(f(x)=\left\{\begin{array}{ll} \int_{0}^{x}(5-|t-3|) d t, & x>4 \\ x^{2}+b x & , x \leq 4
\end{array}\right.\)
where \(b \in R\). If \(f\) is continuous at \(x=4\), then which of the following statements is NOT true?JEE Mains 2022 Hard - Let A and B be the two points of intersection of the line \(y+5=0\) and the mirror image of the parabola \(y^2=4 x\) with respect to the line \(x+y+4=0\). If d denotes the distance between A and B , and a denotes the area of \(\triangle S A B\), where \(S\) is the focus of the parabola \(y^2=4 x\), then the value of \((a+d)\) is \(\qquad\) -JEE Mains 2025 Hard
More PYQs from JEE Mains
- Let \(f(1) = -2\) and \(f'(x) \ge 4.2\) for \(1 \le x \le 6\). The possible value of \(f(6)\) lies in the intervalJEE Mains 2013 Hard
- The sum of the \(3^{rd}\) and the \(4^{th}\) terms of a \(G.P.\) is \(60\) and the product of its first three terms is \(1000\). If the first term of this \(G.P.\) is positive, then its \(7^{th}\) term isJEE Mains 2015 Hard
- If the foot of the perpendicular from point \((4,3,8)\) on the line \(L _{1}: \frac{ x - a }{l}=\frac{ y -2}{3}=\frac{ z - b }{4},\) \(l \neq 0\) is \((3,5,7),\) then the shortest distance between the line \(L _{1}\) and line \(L _{2}: \frac{ x -2}{3}=\frac{ y -4}{4}=\frac{ z -5}{5}\) is equal to:JEE Mains 2021 Hard
- Let \(Q\) be the foot of the perpendicular from the point \(\mathrm{P}(7,-2,13)\) on the plane containing the lines \(\frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8}\) and \(\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-3}{7}\) Then \((\mathrm{PQ})^{2}\), is equal to ..... .JEE Mains 2021 Hard
- Let a random variable X take values \(0,1,2,3\) with \(\mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)=\mathrm{p}, \mathrm{P}(\mathrm{X}=2)=\mathrm{P}(\mathrm{X}=3)\) and \(\mathrm{E}\left(\mathrm{X}^2\right)=2 \mathrm{E}(\mathrm{X})\). Then the value of \(8 \mathrm{p}-1\) is :JEE Mains 2025 Easy
- If the sum of squares of all real values of \(\alpha\), for which the lines \(2 x-y+3=0,6 x+3 y+1=0\) and \(\alpha x+2 y-2=0\) do not form a triangle is \(p\), then the greatest integer less than or equal to \(\mathrm{p}\) is \(.........\)JEE Mains 2024 Medium