JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the acute angle bisector of the two planes \(x-2 y-2 z+1=0\) and \(2 x-3 y-6 z+1=0\) be the plane \(\mathrm{P}\). Then which of the following points lies on \(\mathrm{P} ?\)
- A \(\left(3,1,-\frac{1}{2}\right)\)
- B \(\left(-2,0,-\frac{1}{2}\right)\)
- C \((0,2,-4)\)
- D \((4,0,-2)\)
Answer & Solution
Correct Answer
(B) \(\left(-2,0,-\frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}_{1}: \mathrm{x}-2 \mathrm{y}-2 \mathrm{z}+1=0\) \(\mathrm{P}_{2}: 2 \mathrm{x}-3 \mathrm{y}-6 \mathrm{z}+1=0\)…
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
- The area (in sq. units) of an equilateral triangle inscribed in the parabola \(\mathrm{y}^{2}=8 \mathrm{x},\) with one of its vertices on the vertex of this parabola, isJEE Mains 2020 Medium
- 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
- The set of values of \(a\) for which \(\lim _{x \rightarrow a}([x-5]-[2 x+2])=0\), where, \([\zeta]\) denotes the greatest integer less than or equal to \(\zeta\) is equal toJEE Mains 2023 Medium
- Let the circles \(C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2\) and \(C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2\) touch each other externally at the point \((6,6)\). If the point \((6,6)\) divides the line segment joining the centres of the circles \(C_1\) and \(C_2\) internally in the ratio \(2: 1\), then \((\alpha+\beta)+4\left(r_1^2+r_2^2\right)\) equalsJEE Mains 2024 Hard
- If the line \(y =4+ kx , k >0\), is the tangent to the parabola \(y = x - x ^{2}\) at the point \(P\) and \(V\) is the vertex of the parabola, then the slope of the line through \(P\) and \(V\) isJEE Mains 2022 Hard
- If \(\mathop {\lim }\limits_{x \to 2} \frac{{\tan \left( {x - 2} \right)\{ {x^2} + (k - 2)x - 2k\} }}{{{x^2} - 4x + 4}} = 5\) , then \(k\) is equal toJEE Mains 2014 Hard
More PYQs from JEE Mains
- Let ABC be the triangle such that the equations of lines \(A B\) and \(A C\) be \(3 y-x=2\) and \(x+y=2\), respectively, and the points B and C lie on x -axis. If \(P\) is the orthocentre of the triangle \(A B C\), then the area of the triangle PBC is equal toJEE Mains 2025 Easy
- If \(8=3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2 p)+\frac{1}{4^3}(3+3 p)+\ldots \infty,\) then the value of \(p\) isJEE Mains 2024 Medium
- Let O be the vertex of the parabola \( x^{2}=4y \) and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2 : 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is:JEE Mains 2026 Medium
- Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a twice differentiable function such that \(f(x+y)=f(x) f(y)\) for all \(x, y \in \mathbf{R}\). If \(f^{\prime}(0)=4 \mathrm{a}\) and \(f\) satisfies \(f^{\prime \prime}(x)-3 \mathrm{a} f^{\prime}(x)-f(x)=0\), \(\mathrm{a}\gt0\), then the area of the region \(\mathrm{R}=\{(x, y) \mid 0 \leq y \leq f(\mathrm{a} x), 0 \leq x \leq 2\}\) is:JEE Mains 2025 Hard
- \(f(x)=4 \log _{e}(x-1)-2 x^{2}+4 x+5, x>1\), which one of the following is NOT correct?JEE Mains 2022 Hard
- Let two fair six-faced dice \(A\) and \(B\) be thrown simultaneously. If \(E_1\) is the event that die \(A\) shows up four, \(E_2 \) is the event that die \(B\) shows up two and \(E_3\) is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true \(?\)JEE Mains 2016 Hard