JEE Mains · Maths · STD 12 - 11. three dimension geometry
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 to
- A \(2\)
- B \(3\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
If \(\lambda=-7,\) then planes will be parallel \& distance between them will be \(\frac{3}{\sqrt{633}} \Rightarrow \mathrm{k}=3\) But if \(\lambda \neq-7,\) then planes will be intersecting and distance between them will be \(0\)
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
- Let \(\overrightarrow{ a }, \overrightarrow{ b }, \overrightarrow{ c }\) be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is \(14\) and \((\vec{a} \times \vec{b}) \cdot(\vec{b} \times \vec{c})+(\vec{b} \times \vec{c}) \cdot(\vec{c} \times \vec{a})+(\vec{c} \times \vec{a}) \cdot(\vec{a} \times \vec{b})=168\) then \(|\vec{a}|+|\vec{b}|+|\vec{c}|\) is equal to.JEE Mains 2022 Hard
- Consider a triangle having vertices \(A(-2,3), B(1,9)\) and \(C(3,8)\). If a line \(L\) passing through the circum-center of triangle \(\mathrm{ABC}\), bisects line \(\mathrm{BC}\), and intersects \(\mathrm{y}\)-axis at point \(\left(0, \frac{\alpha}{2}\right)\), then the value of real number \(\alpha\) is \(.....\)JEE Mains 2021 Hard
- Let the set of all positive values of \(\lambda\), for which the point of local minimum of the function \(\left(1+x\left(\lambda^2-x^2\right)\right)\) satisfies \(\frac{x^2+x+2}{x^2+5 x+6}<0\), be \((\alpha, \beta)\). Then \(\alpha^2+\beta^2\) is equal to ...........JEE Mains 2024 Hard
- The sum of the series \(\frac{1}{1-3 \cdot 1^2+1^4}+\) \(\frac{2}{1-3 \cdot 2^2+2^4}+\frac{3}{1-3 \cdot 3^2+3^4}+\ldots\). up to \(10\) terms isJEE Mains 2024 Hard
- Suppose a, b, c are in A.P. and \( a^{2}, 2b^{2}, c^{2} \) are in G.P. If \( a < b < c \) and \( a+b+c=1, \) then \( 9(a^{2}+b^{2}+c^{2}) \) is equal to ___ .JEE Mains 2026 Easy
- If \(y=\frac{(\sqrt{x}+1)\left(x^2-\sqrt{x}\right)}{x \sqrt{x}+x+\sqrt{x}}+\frac{1}{15}\left(3 \cos ^2 x-5\right) \cos ^3 x\), then \(96 y^{\prime}\left(\frac{\pi}{6}\right)\) is equal to :JEE Mains 2024 Hard
More PYQs from JEE Mains
- If three letters can be posted to any one of the \(5\) different addresses, then the probability that the three letters are posted to exactly two addresses is :JEE Mains 2024 Medium
- The number of distinct real roots of the equation \(x ^{7}-7 x -2=0\) isJEE Mains 2022 Hard
- If the sum of the coefficients of \(x^7\) and \(x^{14}\) in the expansion of \(\left(\dfrac{1}{x^3} - x^4\right)^n\), \(x \neq 0\), is zero, then the value of \(n\) is __________.JEE Mains 2026 Hard
- Let \(P Q R\) be a triangle with \(R(-1,4,2)\). Suppose \(M(2,1,2)\) is the mid point of \(PQ\). The distance of the centroid of \(\triangle \mathrm{PQR}\) from the point of intersection of the line \(\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}\) and \(\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}\) isJEE Mains 2024 Medium
- If \( \int_{0}^{1}4~cot^{-1}(1-2x+4x^{2})dx=a~tan^{-1}(2)-b~log_{c}(5), \) where a, b \( \in N \), then \( (2a+b) \) is equal to :JEE Mains 2026 Hard
- The domain of the function \(f(x)=\frac{\cos ^{-1}\left(\frac{x^{2}-5 x+6}{x^{2}-9}\right)}{\log _{e}\left(x^{2}-3 x+2\right)} \text { is }\)JEE Mains 2022 Hard