Distance between the two planes: 2x+3y+4z = 4 and 4x+6y+8z = 12 is
Distance between the two planes: 2x+3y+4z = 4 and 4x+6y+8z = 12 is
2 units
- 4 units
- 8 units
\(\frac {2}{\sqrt 29}\) units
The Correct Option is D
Solution and Explanation
The equation of the planes are
2x+3y+4z = 4 ...(1)
4x+6y+8z = 12
⇒2x+3y+4z = 6 ...(2)
It can be seen that the given planes are parallel. It is known that the distance between two parallel planes, ax+by+cz=d1 and ax+by+cz=d2, is given by,
D = \(|\frac {d_2-d_1}{√a^2+b^2+c^2}|\)
⇒ D = \(|\frac {6-4}{√2^2+3^2+4^2}|\)
D = \(\frac {2}{\sqrt 29}\)
Thus, the distance between the lines is \(\frac {2}{\sqrt 29}\) units.
Hence, the correct answer is D.
Top Questions on Three Dimensional Geometry
- Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Three Dimensional Geometry
The vector equations of two lines are given as:
Line 1: \[ \vec{r}_1 = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(4\hat{i} + 6\hat{j} + 12\hat{k}) \]
Line 2: \[ \vec{r}_2 = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(6\hat{i} + 9\hat{j} + 18\hat{k}) \]
Determine whether the lines are parallel, intersecting, skew, or coincident. If they are not coincident, find the shortest distance between them.
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Three Dimensional Geometry
Show that the following lines intersect. Also, find their point of intersection:
Line 1: \[ \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} \]
Line 2: \[ \frac{x - 4}{5} = \frac{y - 1}{2} = z \]
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Three Dimensional Geometry
Determine the vector equation of the line that passes through the point \( (1, 2, -3) \) and is perpendicular to both of the following lines:
\[ \frac{x - 8}{3} = \frac{y + 16}{7} = \frac{z - 10}{-16} \quad \text{and} \quad \frac{x - 15}{3} = \frac{y - 29}{-8} = \frac{z - 5}{-5} \]
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Three Dimensional Geometry
- Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.
- MHT CET - 2025
- Mathematics
- Three Dimensional Geometry
Questions Asked in CBSE CLASS XII exam
- Your school is organising an inter-house ‘Maths Quiz’ Competition. As president of the Quiz Club, draft a notice informing students of Classes IX – XII about the competition. Include necessary details regarding the number of participants, registration date, etc. You are Akila / Akhil. Put your notice in a box.
- CBSE CLASS XII - 2025
- Writing Skills
Draw a rough sketch for the curve $y = 2 + |x + 1|$. Using integration, find the area of the region bounded by the curve $y = 2 + |x + 1|$, $x = -4$, $x = 3$, and $y = 0$.
- CBSE CLASS XII - 2025
- Integration
- Find the local maxima and local minima of the function \[ f(x) = \frac{8}{3} x^3 - 12x^2 + 18x + 5. \]
- CBSE CLASS XII - 2025
- Differentiation
- Figure shows variation of Coulomb force (F) acting between two point charges with \( \frac{1}{r^2} \), \( r \) being the separation between the two charges \( (q_1, q_2) \) and \( (q_2, q_3) \). If \( q_2 \) is positive and least in magnitude, then the magnitudes of \( q_1, q_2 \), and \( q_3 \) are such that:
- CBSE CLASS XII - 2025
- Electrostatics
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.
- CBSE CLASS XII - 2025
- Relations and Functions