TS EAMCET · Maths · Three Dimensional Geometry
A plane passes through \((2,3,-1)\) and is perpendicular to the line having direction ratios \(3,-4,7\). The perpendicular distance from the origin to this plane is
- A \(\frac{3}{\sqrt{74}}\)
- B \(\frac{5}{\sqrt{74}}\)
- C \(\frac{6}{\sqrt{74}}\)
- D \(\frac{13}{\sqrt{74}}\)
Answer & Solution
Correct Answer
(D) \(\frac{13}{\sqrt{74}}\)
Step-by-step Solution
Detailed explanation
The equation of the plane passes through the point \((2,3,-1)\) is \(a(x-2)+b(y-3)+c(z+1)=0\) ...(i) where \(a, b, c\) are the direction ratio of the normal to the plane. Also, given the plane is perpendicular to the line whose direction ratio is \((3,-4,7)\). So, that line and…
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 points with position vectors \(\hat{i}-\hat{j}+\hat{k}, 2 \hat{i}-\hat{k}, \hat{j}+2 \hat{k}\) and \(\hat{i}+\hat{j}+\lambda \hat{k}\) are coplanar, then the magnitude of the vector \(6 \lambda \hat{i}-3 \hat{j}+6 \hat{k}\) isTS EAMCET 2023 Easy
- \(P, Q, R\) and \(S\) are four points with the position vectors \(3 \mathbf{i}-4 \mathbf{j}+5 \mathbf{k},-4 \mathbf{i}+5 \mathbf{j}+\mathbf{k}\) and \(-3 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k}\), respectively. Then, the line \(P Q\) meets the line \(R S\) at the pointTS EAMCET 2013 Medium
- If \(\Delta\) is the area of the triangle formed by the positive \(x\)-axis and the normal and tangent to the circle \(x^2+y^2=4\) at \((1, \sqrt{3})\), then \(\Delta\) is equal toTS EAMCET 2012 Hard
- If the pair of straight lines given by \(A x^2+2 H x y+B y^2=0\left(H^2>A B\right)\) forms an equilateral triangle with line \(a x+b y+c=0\), then \((A+3 B)(3 A+B)\) is equal to :TS EAMCET 2003 Medium
- If the vectors and are collinear, thenTS EAMCET 2021 Easy
- If \(\omega\) is a complex cube root of unity, then \(\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}\) is equal toTS EAMCET 2008 Medium
More PYQs from TS EAMCET
- A metal has \(9 \times 10^{28}\) conduction electrons per \(\mathrm{m}^3\) and its resistivity is \(1 \times 10^{-8} \Omega\). m. If the drift speed of an electron in the metal is \(1.6 \times 10^6 \mathrm{~m} / \mathrm{s}\) then its mean free path is (mass of electron \(=9 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) )TS EAMCET 2022 Hard
- If the point lies on the locus of satisfying the inequality then the interval in which lies isTS EAMCET 2019 Medium
- If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are three non-collinear points and \(k \mathbf{a}+2 \mathbf{b}+3 \mathbf{c}\) is a point in the plane of \(\mathbf{a}, \mathbf{b}, \mathbf{c}\), then \(k=\)TS EAMCET 2019 Easy
- Number of solutions of the equation \(\tan ^2 x+3 \cot ^2 x=2 \sec ^2 x\) lying in the interval \([0,2 \pi]\) isTS EAMCET 2025 Medium
- A system consists of two particles of masses \(m_1\) and \(m_2\). If the particle of mass \(m_1\) is moved towards the centre of mass through a distance \(d\), then the distance the second particle should be moved, so as to keep the centre of mass at the same position isTS EAMCET 2023 Medium
- A body of mass \(1 \mathrm{~g}\) and carrying a charge \(10^{-8} \mathrm{C}\) passes from two points \(P\) and \(Q . P\) and \(Q\) are at electric potentials. \(600 \mathrm{~V}\) and \(0 \mathrm{~V}\), respectively. The velocity of the body at \(Q\) is \(20 \mathrm{cms}^{-1}\). It velocity in \(\mathrm{ms}^{-1}\) at \(P\) isTS EAMCET 2002 Medium