Question:
The distance from the point (2, 2, 2) to the plane 2x-y+3z = 5 is equal to
The distance from the point (2, 2, 2) to the plane 2x-y+3z = 5 is equal to
Updated On: May 31, 2024
- \(\frac{3\sqrt{7}}{2}\)
- \(\frac{\sqrt{3}}{2}\)
- \(\frac{3\sqrt{14}}{7}\)
- \(\frac{3\sqrt{14}}{14}\)
- \(\frac{\sqrt{3}}{3}\)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D) : \(\frac{3\sqrt{14}}{14}\)
Was this answer helpful?
0
0
Top Questions on Three Dimensional Geometry
- A straight line drawn from the point P(1,3, 2), parallel to the line \(\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}\), intersects the plane L1 : x - y + 3z = 6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1 intersects the plane L2 : 2x - y + z = -4 at the point R. Then which of the following statements is (are) TRUE ?
- JEE Advanced - 2024
- Mathematics
- Three Dimensional Geometry
- Let y ∈ R be such that the lines \(L_1:\frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3}\) and \(L_2:\frac{x+16}{3}=\frac{y+11}{2}=\frac{z+4}{\gamma}\) intersect. Let R1 be the point of intersection of L1 and L2. Let O = (0, 0 ,0), and \(\hat{n}\) denote a unit normal vector to the plane containing both the lines L1 and L2.
Match each entry in List-I to the correct entry in List-II.The correct option isList - I List - II (P) γ equals (1) \(-\hat{i}-\hat{j}+\hat{k}\) (Q) A possible choice for \(\hat{n}\) is (2) \(\sqrt{\frac{3}{2}}\) (R) \(\overrightarrow{OR_1}\) equals (3) 1 (S) A possible value of \(\overrightarrow{OR_1}.\hat{n}\) is (4) \(\frac{1}{\sqrt6}\hat{i}-\frac{2}{\sqrt6}\hat{j}+\frac{1}{\sqrt6}\hat{k}\) (5) \(\sqrt{\frac{2}{3}}\) - JEE Advanced - 2024
- Mathematics
- Three Dimensional Geometry
- Let R3 denote the three-dimensional space. Take two points P = (1, 2, 3) and Q = (4, 2 ,7). Let
dist(X, Y) denote the distance between two points X and Y in R3. Let
\(S=\left\{X\in\R^3:(dist(X,P)^2)-(dist(X,Q))^2=50\right\}\ and\)
\(T=\left\{Y\in \R^3:(dist(Y,Q))^2-(dist(Y,P))^2=50\right\}\)
Then which of the following statements is (are) TRUE ?- JEE Advanced - 2024
- Mathematics
- Three Dimensional Geometry
- If the foot is perpendicular from (1, 2, 3) to the line \(\frac{x+1}{2} = \frac{y-2}{5} = \frac{z-1}{1}\) is \(( a, \beta, \gamma)\), then find \(a + \beta + \gamma\)
- JEE Main - 2024
- Mathematics
- Three Dimensional Geometry
- ABC is an isosceles triangle with an inscribed circle with center O. Let P be the midpoint of BC. If AB=AC=15 and BC=10,then OP equals
- WBJEE - 2023
- Mathematics
- Three Dimensional Geometry
View More Questions
Questions Asked in KEAM exam
- A Spherical ball is subjected to a pressure of 100 atmosphere. If the bulk modulus of the ball is 1011 N/m2,then change in the volume is:
- KEAM - 2023
- mechanical properties of solids
- Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0. Then mass of each sphere is:
- KEAM - 2023
- System of Particles & Rotational Motion
- The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are
- KEAM - 2023
- Trigonometric Functions
- \(∫xlog(1+x^2)dx=\)?
- KEAM - 2023
- Integration by Parts
- A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of:
- KEAM - 2023
- System of Particles & Rotational Motion
View More Questions