Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) Equations of line through $(5, -4, 6)$ with direction ratios $3, 7, 2$ | (I) $\frac{x+3}{5} = \frac{y+7}{-4} = \frac{z+2}{6}$ | | (B) Equations of line through $(3, 7, 2)$ with direction ratios $5, -4, 6$ | (II) $\frac{x-3}{5} = \frac{y-7}{-4} = \frac{z-2}{6}$ | | (C) Equations of line through $(-5, 4, -6)$ with direction ratios $3, 7, 2$ | (III) $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ | | (D) Equations of line through $(-3, -7, -2)$ with direction ratios $5, -4, 6$ | (IV) $\frac{x+5}{3} = \frac{y-4}{7} = \frac{z+6}{2}$ | Choose the correct answer from the options given below:

The foot of perpendicular from point $(2, 4, -1)$ on the line $\frac{x+5}{1} = \frac{y+3}{4} = \frac{z-6}{-9}$ is :

The equation of line passing through the points (2, -1, 3) and (4, 2, 1) is

(A) $\frac{x-2}{2} = \frac{y+1}{3} = \frac{z-3}{-2}$

(B) $\frac{x-4}{3} = \frac{y-2}{-2} = \frac{z-1}{2}$

(C) $\vec{r} = (2\hat{i}-\hat{j}+3\hat{k}) + \lambda(2\hat{i}+3\hat{j}-2\hat{k})$

(D) $\frac{x-4}{-2} = \frac{y-2}{-3} = \frac{z-1}{2}$

Choose the correct answer from the options given below:

If the vertices of a triangle ABC are $A(1, 2, 1)$, $B(4, 2, 3)$ and $C(2, 3, 1)$, then the equation of the median passing through the vertex $A$, is

The co-ordinates of the point at which the line $\frac{x-3}{3} = \frac{y+1}{2} = \frac{z-4}{-2}$ crosses x-y plane, are

The distance between the two lines $L_1$ and $L_2$ given by $L_1: \dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{-z-4}{-6}$ and $L_2: \dfrac{x-3}{2} = \dfrac{y-3}{3} = \dfrac{z+5}{6}$ is

The value of $\lambda$ so that the lines $\frac{1-x}{3} = \frac{7y-14}{2\lambda} = \frac{z-3}{2}$ and $\frac{7-7x}{3\lambda} = \frac{y-5}{1} = \frac{6-z}{5}$ are at right angle, is: