Line and a Point

The reflection of the point $A\left(1,0,0\right)$ in the line $\frac{x-1}{2}=\frac{y+1}{-3}=-\frac{z+10}{8}$ is

The length of the perpendicular from the point $\left(1,2,3\right)$ to the line $\frac{-x+6}{-3}=\frac{y-7}{2}=\frac{z-7}{-2}$ is _________.

The perpendicular distance of the point $P(2, 1, 3)$ from the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ is

The coordinate of a point on the line $\frac{x-2}{1}=\frac{y+1}{-1}=\frac{z}{3}$ at a distance $\sqrt{21}$ from the point $\left(-1, -1, 1\right)$ is -

The length of the perpendicular from $A(2,-3,1)$ on the line$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$ is

Length of the perpendicular from the point $\left(5,4,-1\right)$ to the line $\overrightarrow{r}=\hat{i}+\lambda (2\hat{i}+9\hat{j}+5\hat{k})$ is

The image of the point (1, 6, 3) in the line $\overrightarrow{r}=\left(\widehat{j}+2\widehat{k}\right)+\lambda \left(\widehat{i}+2\widehat{j}+3\widehat{k}\right)$ is

Find two points on the line $\frac{x-2}{1}=\frac{y+3}{-2}=\frac{z+3}{2}$ which are on either side of $\left(2,-3,-3\right)$ at a distance of $3$ units from it.

Find the length of the perpendicular from the point $\left(5,4,-1\right)$ to the line $\overline{r}=\hat{i}+\lambda (2\hat{i}+9\hat{j}+5\hat{k})$.

Find the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$.Also, find the length of the perpendicular.

The perpendicular distance of the line $\frac{x-4}{2}=\frac{y}{1}=\frac{z-2}{-1}$ from the point $P(1, 1, 3)$ is equal to

The coordinates of the foot of perpendicular from the point $\left(1,0,0\right)$ to the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}$ are

The perpendicular distance of point $P(0,-1,3)$ from the straight line passing through $A(1,-3,2)$ and $B(2,-1,4)$ is

Let $x + y - z – 4 = 0$ be the equation of a plane and $A$ be a point $(1, 2, –3)$. If line L passes through $(1, 2, 3)$ with direction ratios $3 : –1 : 4.$ If distance of $\mathrm{A}$ from line measured parallel to the plane is $d_1$ and if distance of the plane measured parallel to line is $d_2$ then $\left(\sqrt{d_1^2-d_2^2}\right)$ is 

The length of the perpendicular from $\left(\mathrm{1,0},2\right)$ on the line $\frac{\mathrm{x}+1}{3}=\frac{\mathrm{y}-2}{-2}=\frac{\mathrm{z}+1}{-1}$ is

Find the foot of perpendicular from the point $\left(2,3,4\right)$ to the line $\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$. Also find the perpendicular distance of the line from the point.

The equation of a line in the plane given by $\pi \equiv 2x-y+z-4=0$ which is perpendicular to the line $l$ whose equation is given by $\frac{x-2}{1}=\frac{y-2}{-1}=\frac{z-3}{-2}$ and which passes through the point of intersection of $l$ and $\pi$ is equal to:

The image of the point $\left(1,6,3\right)$ in the line represented by $\overrightarrow{r}=\left(\widehat{j}+2\widehat{k}\right)+\lambda \left(\widehat{i}+2\widehat{j}+3\widehat{k}\right)$ is :

Let $O$ be origin and point $P_1\left(1,1,1\right)$ lie on $L_1:x=y=z.$ Projection of $O{P}_1$ on $x$-axis be $O{M}_1$ . Projection of $O{M}_1$ on $L_1$ be $O{P}_2$ and so on then  $\left|P_1{M}_1\right|+\left|P_2{M}_2\right|+......\infty =$______