Angle between a Line and a Plane

The coordinate of the point where the line $\frac{x+1}{2}=\frac{y+2}{3}=\frac{z+3}{4}$ meets the plane $x+y+4z=6$ is

Find the value of $m$, if the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z+1}{2}$ is parallel to the plane $3x-2y+mz=12$.

The angle between the line $\frac{x+1}{2}=\frac{y+4}{3}=\frac{z}{6}$ and the plane $10x+2y-11z=3$ is

Cotyledons are also called-

The distance of the point (1, -5, 9), from the plane $\overrightarrow{r} \cdot \left(\widehat{i}- \widehat{j}+ \widehat{k}\right)=5$ measured along the line $\overrightarrow{r}= \widehat{i}+ \widehat{j}+ \widehat{k}$ is

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

The line $\frac{x-3}{2}=\frac{y-4}{3}=\frac{z-5}{4}$ lies in the plane $4x+4y-kz-d=0$. The values of $k$ and $d$ are

The distance of the point of intersection of the line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ and the plane $x+y+z=17$ from the point $\left(3, 4, 5\right)$ is given by

The line joining the points $\left(3,\mathrm{ }5,\mathrm{ }-7\right)$ and $\left(-2,\mathrm{ }1,\mathrm{ }8\right)$ meets the $yz$ -plane at point

The angle between the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and the plane $3x+2y-3z=4$ is

The co-ordinates of the point where the line $\frac{x-6}{-1}=\frac{y+1}{0}=\frac{z+3}{4}$ meets the plane $x+y-z=3$ are

The angle between the line $\frac{x-2}{a}=\frac{y-2}{b}=\frac{z-2}{c}$ and the plane $ax+by+cz+6=0$ is

The line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is parallel to the plane

If line $\frac{x-x_1}{\mathrm{l}}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$ is parallel to the plane $ax+by+cz+d=0$ , then

The line $\frac{x+3}{3}=\frac{y-2}{-2}=\frac{z+1}{1}$ and the plane $4x+5y+3z-5=0$ intersect at a point

The equation of the plane which bisects the line joining the points $\left(-1,\mathrm{ }2,\mathrm{ }3\right)$ and $\left(3,\mathrm{ }-5,\mathrm{ }6\right)$ at right angle, is

The point at which the line joining the points $\left(2,\mathrm{ }-3,\mathrm{ }1\right)$ and $\left(3,\mathrm{ }-4,\mathrm{ }-5\right)$ intersects the plane $2x+y+z=7$ is

The equation of a plane parallel to $x$- axis is

The equation of the plane passing through the intersection of the planes $x+y+z=6$ and $2x+3y+4z+5=0$ the point $\left(1, 1, 1\right)$ , is

A line passing through $A (1, 2, 3)$ and having direction ratios $(3, 4, 5)$ meets a plane $x + 2y – 3z = 5$ at $B$, then distance $AB$ is equal to -