JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the image of the point \( P(a,2,a) \) in the line \( \frac{x}{2}=\frac{y+a}{1}=\frac{z}{1} \) is Q and the image of Q in the line \( \frac{x-2b}{2}=\frac{y-a}{1}=\frac{z+2b}{-5} \) is P, then \( a+b \) is equal to:
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\(\frac{2 \lambda-a+a}{2}=-5 \mu-2 b\) and \(\frac{a+4 \lambda-a}{2}=2 \mu+2 b\) and \(\frac{2 \lambda-2 a-2+2}{2}=\mu+a\) \(\Rightarrow \lambda-\mu= b\) \(\lambda-\mu=2 a\) \(\lambda+5 \mu=-2 b\) \(\Rightarrow b =2 a\) and \(\lambda= a , \mu=- a\)…
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
- Let \({f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\;,x \in R\) and \(k \ge 1\), then \({f_4}\left( x \right) - {f_6}\left( x \right)\) is equal toJEE Mains 2014 Hard
- If \(y=y(x)\) is the solution of the differential equation \(\frac{d y}{d x}+2 y=\sin (2 x), y(0)=\frac{3}{4}\), then \(\mathrm{y}\left(\frac{\pi}{8}\right)\) is equal to :JEE Mains 2024 Medium
- If the coefficients of \(x^2\) and \(x^3\) are both zero, in the expansion of the expression \((1 + ax + bx^2) (1 -3x)^{t5}\) in powers of \(x\), then the ordered pair \((a, b)\) is equal toJEE Mains 2019 Hard
- If \( \cot x=\frac{5}{12} \) for some \( x\in(\pi,\frac{3\pi}{2}) \), then \( \sin 7x(\cos\frac{13x}{2}+\sin\frac{13x}{2}) + \cos 7x(\cos\frac{13x}{2}-\sin\frac{13x}{2}) \) is equal toJEE Mains 2026 Hard
- In a tournament, a team plays \(10\) matches with probabilities of winning and losing each match as \(\frac{1}{3}\) and \(\frac{2}{3}\) respectively. Let \(x\) be the number of matches that the team wins, and \(y\) be the number of matches that team loses. If the probability \(\mathrm{P}(|\mathrm{x}-\mathrm{y}| \leq 2)\) is \(\mathrm{p}\), then \(3^9 \mathrm{p}\) equals ...........JEE Mains 2024 Hard
- Let a smooth curve \(y=f(x)\) be such that the slope of the tangent at any point \((x, y)\) on it is directly proportional to \(\left(\frac{-y}{x}\right)\). If the curve passes through the point \((1,2)\) and \((8,1)\), then \(\left| y \left(\frac{1}{8}\right)\right|\) is equal toJEE Mains 2022 Hard
More PYQs from JEE Mains
- Let the solution curve of the differential equation \(xdy-ydx=\sqrt{x^{2}+y^{2}}dx, x>0, y(1)=0\), be \(y=y(x)\). Then \(y(3)\) is equal toJEE Mains 2026 Medium
- Let the direction cosines of two lines satisfy the equations: \( 4l+m-n=0 \) and \( 2mn+10nl+3lm=0 \). Then the cosine of the acute angle between these lines is:JEE Mains 2026 Easy
- The area (in sq. units) of the smaller portion enclosed between the curves, \(x^2 + y^2 = 4\) and \(y^2 =3x\), isJEE Mains 2017 Hard
- Let \(z \in C\) the set of complex numbers. Then the equation, \(2\left| {z + 3i} \right| - \left| {z - i} \right| = 0\) representsJEE Mains 2017 Hard
- If the projection of the vector \(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) on the sum of the two vectors \(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}\) and \(-\lambda \hat{i}+2 \hat{j}+3 \hat{k}\) is \(1,\) then \(\lambda\) is equal to ..... .JEE Mains 2021 Medium
- Let \(R\) be a relation defined on \(N\) as a \(R\) b is \(2 a+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) isJEE Mains 2023 Medium