AP EAMCET · Maths · Three Dimensional Geometry
The angle between the planes \(2 x-y+z=6\) and \(x+y+2 z=3\) is
- A \(\frac{\pi}{3}\)
- B \(\cos ^{-1}\left(\frac{1}{6}\right)\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Given, planes are \(2 x-y+z=6\) and \(x+y+2 z=3\) General equation of plane is \(a x+b y+c z=d\) Normal vector of plane is \(a \hat{\mathrm{i}}+b \hat{\mathrm{j}}+c \hat{\mathrm{k}}\). For plane \(2 x-y+z=6\)…
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 the probability distribution of a random variable X is as follows, then \(\mathrm{k}=\)
\begin{array}{|c|c|c|c|c|}\hline \boldsymbol{X}=\boldsymbol{x} & 1 & 2 & 3 & 4 \\\hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & 2 k & 4 k & 3 k & k \\\hline\end{array}AP EAMCET 2024 Easy - If \(\lim _{x \rightarrow 0} \frac{e^x-a-\log (1+x)}{\sin x}=0\) then \(a=\)AP EAMCET 2024 Easy
- The value of '' for which the equation represents a pair of straight lines, isAP EAMCET 2021 Easy
- Let \(\pi_1\) be the plane determined by the vectors \(\hat{i}+\hat{j}\) and \(\hat{j}+\hat{k}, \pi_2\) be the plane determined by the vectors \(\hat{i}-\hat{j}\) and \(\hat{i}+\hat{j}-\hat{k}\). Let \(\vec{a}\) be a vector parallel to the line of intersection of \(\pi_1\) and \(\pi_2\). If \(|\vec{a}|=\sqrt{14}\), then \(|\vec{a} \cdot(\hat{i}+\hat{j}+\hat{k})|=\)AP EAMCET 2023 Easy
- \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+3 x^2-10 x-24=\) 0 . If \(\alpha(\beta+\gamma), \beta(\gamma+\alpha)\) and \(\gamma(\alpha+\beta)\) are the roots of the equation \(x^3+p x^2+q x+r=0\), then \(q=\)AP EAMCET 2024 Medium
- \(\int \frac{x}{\sqrt{x+1}+\sqrt{x-1}} d x=A(x)(x+1)^{\frac{3}{2}}+B(x)(x-1)^{\frac{3}{2}}+C\) , then \(A(x)+B(x)=\)AP EAMCET 2019 Hard
More PYQs from AP EAMCET
- If \(\left[\begin{array}{lll}x & 4-1\end{array}\right]\left[\begin{array}{lll}2 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & 4\end{array}\right]\left[\begin{array}{c}x \\ 4 \\ -1\end{array}\right]=0\), then \(x=\)AP EAMCET 2023 Easy
- If \(\cos \theta \neq 0\), and \(\sec \theta-1=(\sqrt{2}-1) \tan \theta\) then \(\theta=\)AP EAMCET 2019 Easy
- If the form of the solution of the differential equation \(\left(y^3+x\right) \frac{d y}{d x}=y\) when \(y(4)=2\) is \(y^3=a x+b\), then \(4 a+12 b^2=\)AP EAMCET 2017 Medium
- \(A\) and \(B\) are independent events of a random experiment if and only ifAP EAMCET 2023 Easy
- If \((1, a),(b, 2)\) are conjugate points with respect to the circle \(x^2+y^2=25\), then \(4 a+2 b\) is equal toAP EAMCET 2004 Easy
- Let be a function satisfying (constant), and ThenAP EAMCET 2022 Hard