TS EAMCET · Maths · Three Dimensional Geometry
If the angle between the planes \(a x-y+3 z=2 a\) and \(3 x+a y+z=3 a\) is \(\frac{\pi}{3}\) then the direction ratios of the line perpendicular to the plane \((a+2) x+(a-4) y+2 a z=a\) are
- A \((2,-1,2)\)
- B \((2,1,-2)\)
- C \((2,1,2)\)
- D \((2,2,-1)\)
Answer & Solution
Correct Answer
(A) \((2,-1,2)\)
Step-by-step Solution
Detailed explanation
\(\vec{n_1} = \langle a, -1, 3 \rangle\), \(\vec{n_2} = \langle 3, a, 1 \rangle\) \(\cos \frac{\pi}{3} = \frac{|\vec{n_1} \cdot \vec{n_2}|}{||\vec{n_1}|| \cdot ||\vec{n_2}||}\) \(\frac{1}{2} = \frac{|3a - a + 3|}{\sqrt{a^2 + 1 + 9}\sqrt{9 + a^2 + 1}}\)…
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
- In a \(\triangle A B C\), the correct formulae among the following areTS EAMCET 2004 Hard
- \(\cos \left(\frac{\pi}{7}\right) \cos \left(\frac{2 \pi}{7}\right) \cos \left(\frac{4 \pi}{7}\right)=\)TS EAMCET 2018 Medium
- If \(x=a(\cos \theta+\theta \sin \theta), y=f(\theta), f(2 \pi)=0\), \(\frac{d y}{d x}=\frac{\tan \theta}{\theta}, \theta \neq 0\) and \(\theta \neq(2 n+1) \frac{\pi}{2}\), then \(f\left(\frac{\pi}{3}\right)=\)TS EAMCET 2022 Easy
- Two dice are rolled. If a random variable \(X\) is defined as the absolute difference of the two numbers that appear on them, then the mean of \(X\) isTS EAMCET 2019 Medium
- The absolute maximum value of the function \(f(x)=2 x^3-3 x^2-36 x+9\) defined on \([-3,3]\) isTS EAMCET 2022 Medium
- Among the positive divisors of the number 12600 , if \(n_1\) is the number of divisors which are multiples of 3 and \(n_2\) is the number of divisors which are multiples of 14 , then \(\mathrm{n}_1+\mathrm{n}_2=\)TS EAMCET 2023 Medium
More PYQs from TS EAMCET
- The mean deviation from the mean 10 of the data \(6,7,11,12,13, \alpha, 12,16\) isTS EAMCET 2017 Easy
- Which of the following is not tetrahedral?TS EAMCET 2007 Easy
- If \(\log (1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots \ldots \infty\) and \(\lim _{x \rightarrow 0} \frac{\log (1+x)^{1+x}}{x^2}-\frac{1}{x}=k\), then \(12 k=\)TS EAMCET 2020 Easy
- The mean deviation about the mean of the following data is nearly
TS EAMCET 2020 Easy - In the List-I each item contains equations of two circles, List-II contains the number of common tangents for each pair of circles given in List-I. Match the items of List-I with those of the items of List-II
The correct match is \(\text { A } \quad \text { B } \quad C \quad \text { D }\) The correct match isTS EAMCET 2020 Medium - The quadratic equation whose roots are \(l\) and \(m\), where \[ \begin{aligned} & l=\lim _{\theta \rightarrow 0}\left(\frac{3 \sin \theta-4 \sin ^2 \theta}{\theta}\right), \ & m=\lim _{\theta \rightarrow 0} \frac{2 \tan \theta}{\theta\left(1-\tan ^2 \theta\right)}, \text { is } \end{aligned} \]TS EAMCET 2002 Hard