List of top Mathematics Questions on Plane asked in MHT CET

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 ______.

The equation of the plane passing through (1,1,1) and through the line of intersection of $x+2y-z+1=0$ and $3x-y-4z+3=0$ is

The unit vectors perpendicular to the plane determined by the points $A(1,-1,2)$, $B(2,0,-1)$, $C(0,2,1)$ is

The direction cosines of a normal to the plane passing through (4, 2, 3), (-1, 4, 2) and (3, 2, 1) are

The equation of plane passing through ( (1, 0, 0) ) and ( (0, 1, 0) ) and making an angle ( 45^\circ ) with the plane ( x + y - 3 = 0 ) is

The X and Y intercepts of the tangent to the hyperbola \(\frac{x^2}{20} - \frac{y^2}{5} = 1\) which is perpendicular to the line \(4x + 3y = 7\), are respectively

If the planes \(\bar{r} \cdot (2\hat{i} - \lambda\hat{j} + \hat{k}) = 3\) and \(\bar{r} \cdot (4\hat{i} - \hat{j} + \mu\hat{k}) = 5\) are parallel, then \(\lambda + \mu =\)

The equation of plane passing through ( (1, 0, 0) ) and ( (0, 1, 0) ) and making an angle ( 45^\circ ) with the plane ( x + y - 3 = 0 ) is

The equation of plane passing through ( (1, 0, 0) ) and ( (0, 1, 0) ) and making an angle ( 45^\circ ) with the plane ( x + y - 3 = 0 ) 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

The foot of the perpendicular drawn from the origin to the plane is $(4,-2,5)$, then the Cartesian equation of the plane is

If a plane meets the axes $X$, $Y$, $Z$ in $A$, $B$, $C$ respectively such that centroid of $\Delta ABC$ is $(1, 2, 3)$, then the equation of the plane is

The plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1$ cuts the $X$-axis at $A$, $Y$-axis at $B$ and $Z$-axis at $C$, then the area of $\Delta ABC$ is

The line $\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}$ lies in the plane $x + 3y - \alpha z + \beta = 0$, then value of $\alpha \beta$ is

The d.r.s. of the normal to the plane passing through the origin and the line of intersection of the planes $x+2y+3z=4$ and $4x+3y+2z=1$ are

The Cartesian equation of a plane which passes through the points $\text{A}(2, 2, 2)$ and making equal nonzero intercepts on the co-ordinate axes is

If $A$ and $B$ are the foot of the perpendicular drawn from the point $Q(a, b, c)$ to the planes $YZ$ and $ZX$ respectively, then the equation of the plane through the points $A$, $B$, and the origin $O$ is

Equation of the plane passing through the point $(1, 2, 3)$ and parallel to the plane $2x + 3y - 4z = 0$ is

The equation of the plane passing through $(-2,2,2)$ and $(2,-2,-2)$ and perpendicular to the plane $9x-13y-3z=0$ is

The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the XY plane is

The equation of the plane containing the line $\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z+2}{1}$ and the point $(0,7,-7)$ is

Equation of the plane passing through the point $(2, 0, 5)$ and parallel to the vectors $\hat{i} - \hat{j} + \hat{k}$ and $3\hat{i} + 2\hat{j} - \hat{k}$ is