Question:
The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the XY plane is
The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the XY plane is
Show Hint
This is a visual shortcut question! A plane parallel to the XY plane locks the Z value. A plane parallel to the YZ plane locks the X value. A plane parallel to the XZ plane locks the Y value. Just grab the corresponding coordinate from the given point!
Updated On: Jun 1, 2026
- $z = 1$
- $y = 8$
- $x = 7$
- $z = 6$
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
We need to find the equation of a 3D plane that is perfectly parallel to the standard XY plane and passes through a specific coordinate point $(7, 8, 6)$.
Step 2: Key Formula or Approach:
The standard equation of the XY plane is $z = 0$, because every single point on the XY plane has a height (z-coordinate) of zero.
Any plane that is parallel to the XY plane will have a constant z-coordinate for all its points. Its general equation is simply $z = c$, where $c$ is a constant.
Step 3: Detailed Explanation:
Since the required plane is parallel to the XY plane, its equation must be of the form $z = c$.
We are given that the plane passes through the point $A(x_1, y_1, z_1) = (7, 8, 6)$.
Because the point lies on the plane, its z-coordinate must satisfy the plane's equation.
Therefore, we plug the z-coordinate of point A into our general equation:
$c = 6$
This means the equation of the entire plane is just $z = 6$.
Step 4: Final Answer:
The Cartesian equation of the plane is $z = 6$, which corresponds to option (D).
We need to find the equation of a 3D plane that is perfectly parallel to the standard XY plane and passes through a specific coordinate point $(7, 8, 6)$.
Step 2: Key Formula or Approach:
The standard equation of the XY plane is $z = 0$, because every single point on the XY plane has a height (z-coordinate) of zero.
Any plane that is parallel to the XY plane will have a constant z-coordinate for all its points. Its general equation is simply $z = c$, where $c$ is a constant.
Step 3: Detailed Explanation:
Since the required plane is parallel to the XY plane, its equation must be of the form $z = c$.
We are given that the plane passes through the point $A(x_1, y_1, z_1) = (7, 8, 6)$.
Because the point lies on the plane, its z-coordinate must satisfy the plane's equation.
Therefore, we plug the z-coordinate of point A into our general equation:
$c = 6$
This means the equation of the entire plane is just $z = 6$.
Step 4: Final Answer:
The Cartesian equation of the plane is $z = 6$, which corresponds to option (D).
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Plane Questions
- The equation of the plane passing through the point \( (1, 1, 1) \) and perpendicular to the planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \) is:
- If one of the lines given by \( 6x^2 - xy + 4cy^2 = 0 \) is \( 3x + 4y = 0 \), then \( c \) equals
- Equation of the plane passing through $(1,-1,2)$ and perpendicular to the planes $x+2y-2z=4$ and $3x+2y+z=6$ is
- The foot of the perpendicular drawn from the origin to the plane is $(4,-2,5)$, then the Cartesian equation of the plane is
- A vector $\vec{n}$ is inclined to X-axis at 45°, Y-axis at 60° and at an acute angle to Z-axis. If $\vec{n}$ is normal to a plane passing through the point $(-\sqrt{2},1,1)$ then equation of the plane is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions