WBJEE · Maths · Three Dimensional Geometry
If the distance between the plane \(a x-2 y+z=k\) and the plane containing the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\) is \(\sqrt{6}\), then \(|k|\) is
- A 36
- B 12
- C 6
- D \(2 \sqrt{3}\)
Answer & Solution
Correct Answer
(C) 6
Step-by-step Solution
Detailed explanation
Hint: Equation of plane \(\begin{aligned} & \left|\begin{array}{ccc} x-1 & y-2 & z-3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{array}\right|=0 \\ & \Rightarrow x-2 y+z=0 \quad ---(1) \end{aligned}\) & given \(\alpha x-2 y+z=k\) ---(2) (1) // (2) \(\Rightarrow \alpha=1, k \neq 0\)…
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
- If \(4 a^2+9 b^2-c^2+12 a b=0\), then the family of straight lines \(a x+b y+c=0\) is concurrent atWBJEE 2023 Medium
- \(\int_0^{2 \pi} \theta \sin ^6 \theta \cos \theta d \theta\) is equal toWBJEE 2023 Medium
- The value of \(\sum_{\mathrm{n}=1}^{10} \int_{-2 n-1}^{-2 \pi} \sin ^{27} x d x+\sum_{n=1}^{10} \int_{2 n}^{2 n+1} \sin ^{27} x d x\) is equal toWBJEE 2020 Medium
- Let \(F(x)=e^{x}, G(x)=e^{-x}\) and \(H(x)=G(F(x)),\) where \(x\) is a real variable. Then, \(\frac{d H}{d x}\) at \(x=0\) isWBJEE 2017 Medium
- A moving line intersects the lines \(x+y=0\) and \(x-y=0\) at the points A, B respectively such that the area of the triangle with vertices \((0,0), A \& B\) has a constant area \(C\). The locus of the mid-point \(A B\) is given by the equationWBJEE 2021 Medium
- Angle between \(\mathrm{y}^2=\mathrm{x}\) and \(\mathrm{x}^2=\mathrm{y}\) at the origin isWBJEE 2009 Medium
More PYQs from WBJEE
- The potential energy of a particle of mass \(0.02 \mathrm{~kg}\) moving along \(x\)-axis is given by \(V=A x(x-4) J\) where \(x\) is in metres and \(\mathrm{A}\) is a constant. Which of the following is/are correct statement(s)?WBJEE 2021 Easy
- If \(0 \leq A \leq \frac{\pi}{4},\) then \(\tan ^{-1}\left(\frac{1}{2} \tan 2 A\right)+\tan ^{-1}(\cot A)+\tan ^{-1}\left(\cot ^{3} A)\right.\)
is equal toWBJEE 2018 Medium - The ozone layer forms naturally byWBJEE 2011 Easy
-
A battery of emf \(\mathrm{E}\) and internal resistance \(\mathrm{r}\) is connected with an external resistance \(\mathrm{R}\) as shown in the figure. The battery will act as a constant voltage source ifWBJEE 2022 Easy - The incentre of an equilateral triangle is (1,1) and the equation of ene side is \(3 x+4 y+3=0 .\) Then, the equation of the circumeircle of the triangle isWBJEE 2012 Medium
- S and \(T\) are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse isWBJEE 2010 Medium