AP EAMCET · Maths · Three Dimensional Geometry
The equation of the plane passing through \((1,1,1)\) and \((1,-1,-1)\) and perpendicular to \(2 x-y+z+5=0\) is :
- A \(2 x+5 y+z+8=0\)
- B \(x+y-z-1=0\)
- C \(2 x+5 y+z+4=0\)
- D \(x-y+z-1=0\)
Answer & Solution
Correct Answer
(B) \(x+y-z-1=0\)
Step-by-step Solution
Detailed explanation
Let the equation of plane passing through \((1,1,1)\) is \(a(x-1)+b(y-1)+c(z-1)=0\) \(\ldots\) (i) It is also passing through \((1,-1,-1)\). \(\therefore \quad a(0)+b(-2)+c(-2)=0\) or \(b+c=0\) \(\ldots\) (ii) Since, Eq. (i) is perpendicular to the plane \(2 x-y+z+5=0\)…
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 \(\mathrm{m} \in \mathrm{Z}^{+}, \mathrm{n}=2 \mathrm{~m}\) and \(\int_0^{\frac{\pi}{2}} \sin ^{\mathrm{m}} \mathrm{x} \cos ^{\mathrm{n}} \mathrm{x} d \mathrm{x}=\mathrm{K}(\mathrm{m})\) \(\int_0^{\frac{\pi}{2}} \sin ^m x d x\), then \(\frac{2^{m-1}(m-1) !}{(2 m-1) !} K(m)=\)AP EAMCET 2023 Hard
- If a random variable X has the following probability distribution, then its variance is nearly
\(\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \mathbf{X}=x: & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline \mathbf{P}(\mathbf{X}=x): & 0.05 & 0.1 & 2 \mathrm{~K} & 0 & 0.3 & \mathrm{~K} & 0.1 \\
\hline
\end{array}\)AP EAMCET 2024 Easy - AP EAMCET 2020 Easy
- The product of the lengths of perpendiculars drawn from any point on the hyperbola \(x^2-2 y^2-2=0\) to its asymptotes is :AP EAMCET 2003 Medium
- The points on the curve \(y=\frac{2}{3} x^3+\frac{1}{2} x^2\), where the tangents make equal angles with coordinate axes areAP EAMCET 2021 Medium
- If \(\alpha\) and \(\beta\) are two distinct negative roots of \(x^5-5 x^3+5 x^2-1=0\), then the equation of least degree with integer coefficients having \(\sqrt{-\alpha}\) and \(\sqrt{-\beta}\) as its roots isAP EAMCET 2024 Medium
More PYQs from AP EAMCET
- Which of the following is not explained by hyperconjugation?AP EAMCET 2021 Easy
- The function \(f(x)=x^3+a x^2+b x+c, a^2 \leq 3 b\) hasAP EAMCET 2009 Medium
- If a random variable \(X\) takes the values \(x_1, x_2, x_3, \ldots, x_{100}\) with probability \(P\left(X=x_i\right)=\) \(K i(i+1)\), then \(200 K=\)AP EAMCET 2020 Medium
- In the Young's double slit experiment, the resultant intensity at a point on the screen is \(75 \%\) of the maximum intensity of the bright fringe. Then the phase difference between the two interfering rays at that point isAP EAMCET 2011 Easy
- For \(n \in Z^{+}\),
\((1+\sin \theta+i \cos \theta)^n+(1+\sin \theta-i \cos \theta)^n=\)AP EAMCET 2018 Hard - The length of the diameter of the circle \(x^2+y^2-6 x-8 y=0\) is unitsAP EAMCET 2020 Easy