List of top Mathematics Questions on Plane asked in MHT CET

If the perpendicular distance of the plane passing through the point \(Q(1,0,-1)\) and containing the line \(\overset{⃗}{r} = (\hat{i}-3\hat{j}+\hat{k})+λ(2\hat{i}-2\hat{j}+\hat{k})\) from origin is \(\frac{p}{\sqrt{53}}\) then \(p =\) ...

If M denotes the midpoint of the line joining A\((4,5,-10)\) and B\((-1,2,1)\), then the equation of the plane through M and perpendicular to AB is:

A plane meets the co-ordinate axes in A, B, C such that the centroid of the triangle ABC is the point \((1,r,r^2)\), then the equation of the plane is,

The perpendicular distance from the origin to the plane containing the points \((1,-2,1),(2,-1,-3)\) and \((0,1,5)\) is...(in units)

The plane \(\frac{x}{2}+\frac{y}{3}+\frac{z}{4} = 1\) cuts the axes at the points A, B, C then the area of triangle ABC is

From a point P \((a,b,c)\), perpendiculars PA and PB are drawn to XY plane and ZX plane respectively. If O is the origin, then the equation of plane OAB is

If the equation of a plane passing through \(A(1,p,2)\), \(B(3,2,4)\) and parallel to the z axis, is \(3x-2y-q = 0\), then \(\ldots\)

The equation of the plane passing through the points having position vectors \((\overset{̄}{a}+\overset{̄}{b}),(\overset{̄}{b}+\overset{̄}{c})\) and \((\overset{̄}{a}+\overset{̄}{c})\) is \(\ldots\)

If the plane \(\overset{̄}{r} = (λ+μ)\hat{i}+(2+μ)\hat{j}+(3λ+2μ)\hat{k}\), where \(λ\) and \(μ\) are parameters, intersects coordinate axes at points \((a,0,0)\), \((0,b,0)\) and \((0,0,c)\) then \(a+b+c =\)...

If the plane \(2x+3y+z = 6\) cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

The acute angle \(θ\) between the \(xy\)-plane and the plane passing through the point \((1,2,4)\) and parallel to the vectors with direction ratios \(3,2,-1\) and \(1,-2,-2\) is...

If A and B are the feet of the perpendiculars drawn from \((1,2,3)\) to planes \(YZ\) and \(ZX\), then the equation of the plane passing through the points A, B and the origin is

If the distance of point \(B(2,1,-3)\) from the line passing through the point \(A(4,-2,2)\), and parallel to the vector \(\overset{⃗}{c} = -4\hat{i}-6\hat{j}-2\hat{k}\) is \(x\), then \(x^4+x^2+541 =\)

The vector equation of plane in parametric form, passing through the points (-1, 2, 0), (2, 2, -1) and parallel to the line \(\frac{x-1}{1} = \frac{2y+1}{2} = \frac{z+1}{-1}\) is

The equation of the plane passing through the point \((1,2,1)\) and perpendicular to the planes \(x+2y+2z-7 = 0\) and \(3x+3y+2z-5 = 0\) is

The equation of the plane containing the lines \(\frac{x-1}{2} = \frac{y+1}{λ} = \frac{z}{2}\) and \(\frac{x+1}{5} = \frac{y+1}{2} = \frac{z}{λ}\) is

The vector equation of the plane which is at a distance of \(5\) units from the origin and normal to the vector \(2\hat{i}+\hat{j}-2\hat{k}\) is

The equation of the plane passing through the intersection of planes \(2x-y+z = 3\), \(4x-3y+5z = -9\) and parallel to the line \(\frac{x+1}{2} = \frac{y+3}{4} = \frac{z-3}{5}\) is...

Let a plane P pass through the point \((3,7,-7)\) and contain the line \(\frac{x-2}{-3} = \frac{y-3}{2} = \frac{z+2}{1}\). If the distance of the plane P from the origin is d, then \(d^2\) is

The plane \(\frac{x}{2}+\frac{y}{3}+\frac{z}{4} = 1\) cuts the co-ordinate axes at the points A, B, C respectively. Then the area of triangle ABC is

The vector equation of the plane passing through the point \(A(-2,7,5)\) and parallel to the vectors \(4\hat{i}-\hat{j}+3\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\) is ...

If the lines \(L_1:\frac{x-1}{-3} = \frac{y-2}{2k} = \frac{z-3}{2},L_2:\frac{x-1}{3k} = \frac{y-5}{1} = \frac{z-6}{-5}\) are perpendicular to each other, then the equation of a plane containing the line \(L_1\) and parallel to the line \(L_2\) for the value of \(k\) that satisfies this condition is ...

A plane meets the coordinate axes at points A, B and C, such that the centroid of a triangle ABC is \((2,-\frac{2}{3},\frac{1}{2})\). The perpendicular distance from the origin to this plane is...

The Cartesian equation of the plane $\vec{r} = (2\hat{i} - 3\hat{j}) + \lambda(\hat{i} + 2\hat{j} - \hat{k}) + \mu(2\hat{i} + 3\hat{j} + \hat{k})$ is \dots}

If the foot of the perpendicular drawn from the origin to a plane is P(-1, -1, 2), then the equation of the plane is ______.