List of top Mathematics Questions on Plane

Plane through (3,5,7), (7,-5,3) parallel to line joining (1,-2,-4) and (4,2,-1) is \(ax+by+cz+80=0\). Then \(a+b+c=\)

The equation of a plane passing through three non-collinear points is determined using:

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

Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L : \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines \( PN \) and \( PQ \), then \( \cos \alpha \) is equal to:

Let the acute angle bisector of the two planes \( x - 2y - 2z + 1 = 0 \) and \( 2x - 3y - 6z + 1 = 0 \) be the plane \( P \). Then which of the following points lies on \( P \)?

Let R be the relation "is congruent to" on the set of all triangles in a plane. Is R:

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

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then

Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is

If the equation of the plane passing through the point $(1,1,2)$ and perpendicular to the line $x-3 y+$ $2 z-1=0=4 x-y+z$ is $A t+ B y+ C z=1$, then $140( C - B + A )$ is equal to______

If \((3,4,-7)\) is the foot of the perpendicular drawn from the point \((-2,3,6)\) to the plane \(\pi\), then the sum of the intercepts made by the plane \(\pi\) on the \(x\)- and \(y\)-axes is