The image of the point (1, 6, 3) with respect to the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is

The foot of the perpendicular drawn from the point $(1,6,3)$ to the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ is

Consider a line $\vec{r} = (\hat{i} + 4\hat{j}) + \lambda(2\hat{i} - 2\hat{j} + 3\hat{k})$, then which of the following statements are correct?

(A) it passes through point (9, -4, 12)

(B) it passes through point (1, 4, -1)

(C) its direction cosine's are $\frac{2}{\sqrt{17}}, \frac{-2}{\sqrt{17}}, \frac{3}{\sqrt{17}}$

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

Choose the correct answer from the options given below:

P is a point on the line segment joining the points (3, 2, -1) and (6, 2, -2) internally. If x coordinate of P is 5, then its z-coordinate is

Points on the line $\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ at a distance of 5 units from the point $(1, 3, 3)$, are

Match List-I with List-II

Choose the correct answer from the options given below:

The equation of plane passing through the point of (3, 2, 0) and containing the line $\frac{x-2}{2} = \frac{y+3}{4} = \frac{z-1}{1}$ is