List of top Mathematics Questions on Plane asked in MET

Equation of a plane passing through \((-1,1,1)\) and \((1,-1,1)\) and perpendicular to \(x + 2y + 2z - 5 = 0\) 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

The line joining the points \( (1,1,2) \) and \( (3,-2,1) \) meets the plane \( 3x + 2y + z = 6 \) at the point

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

If \(\theta\) be the angle between the unit vectors \(\mathbf{a}\) and \(\mathbf{b}\), then \(\cos \frac{\theta}{2}\) is equal to

The maximum value of \((\cos \alpha_1) \cdot (\cos \alpha_2) \cdots (\cos \alpha_n)\) under the restrictions \(0 \leq \alpha_1, \alpha_2, \ldots, \alpha_n \leq \frac{\pi}{2}\) and \((\cot \alpha_1) \cdot (\cot \alpha_2) \cdots (\cot \alpha_n) = 1\) 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: