Question:
The line joining the points \( (1,1,2) \) and \( (3,-2,1) \) meets the plane \( 3x + 2y + z = 6 \) at the point
The line joining the points \( (1,1,2) \) and \( (3,-2,1) \) meets the plane \( 3x + 2y + z = 6 \) at the point
Show Hint
To check if a point lies on a plane, directly substitute coordinates into the plane equation.
Updated On: Apr 23, 2026
- \( (1,1,2) \)
- \( (3,-2,1) \)
- \( (2,-3,1) \)
- \( (3,2,1) \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Check which point satisfies the plane equation.
Step 1: Substitute point \( (1,1,2) \). \[ 3(1) + 2(1) + 2 = 7 \neq 6 \]
Step 2: Substitute point \( (3,-2,1) \): \[ 3(3) + 2(-2) + 1 = 9 - 4 + 1 = 6 \] Final Answer: \[ (3,-2,1) \]
Step 1: Substitute point \( (1,1,2) \). \[ 3(1) + 2(1) + 2 = 7 \neq 6 \]
Step 2: Substitute point \( (3,-2,1) \): \[ 3(3) + 2(-2) + 1 = 9 - 4 + 1 = 6 \] Final Answer: \[ (3,-2,1) \]
Was this answer helpful?
0
0
Top MET Mathematics Questions
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- The equation $3^{3x + 4} = 9^{2x - 2},\ x>0$ has the solution
- A parallelogram is constructed on the vectors $\mathbf{a} = 3\alpha - \beta$, $\mathbf{b} = \alpha + 3\beta$. If $|\alpha| = |\beta| = 2$ and the angle between $\alpha$ and $\beta$ is $\dfrac{\pi}{3}$, then the length of a diagonal of the parallelogram is
- Every group of order 7 is
- Let $U_{n} = 2 + 2^{3} + 2^{5} + \cdots + 2^{2n+1}$ and $V_{n} = 1 + 4 + 4^{2} + \cdots + 4^{n-1}$. Then $\displaystyle\lim_{n \to \infty} \dfrac{U_n}{V_n}$ is equal to
View More Questions
Top MET Plane Questions
- Equation of a plane passing through \((-1,1,1)\) and \((1,-1,1)\) and perpendicular to \(x + 2y + 2z - 5 = 0\) is
- The image of the point with position vector \[ \mathbf{i} + 3 \mathbf{k} \] in the plane \( \mathbf{r} \cdot (\mathbf{i} + \mathbf{j} + \mathbf{k}) = 1 \) is:
- The equation of the plane passing through a point \( A(2, -1, 3) \) and parallel to the vectors \[ \mathbf{a} = (3, 0, -1) \quad \text{and} \quad \mathbf{b} = (-3, 2, 2) \] is:
- The image of the point with position vector \( \hat{i} + 3\hat{k} \) in the plane \( \vec{r}\cdot(\hat{i} + \hat{j} + \hat{k}) = 1 \) is
- The equation of the plane through the intersection of the planes \( 3x - y + 2z - 4 = 0 \) and \( x + y + z - 2 = 0 \) and the point \( (2,2,1) \) is
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions