Find the distance of the point $(-1, -5, -10)$ from the point of intersection of the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$.

The equation of a line parallel to the vector \(3\hat{i}+\hat{j}+2\hat{k}\) and passing through the point \((4, -3, 7)\) is:

Find the vector and the Cartesian equations of a line passing through the point (1,2,-4) and parallel to the line joining the points A(3,3,-5) and B(1,0,-11). Hence, find the distance between the two lines. OR Find the equations of the line passing through the points A(1,2,3) and B(3,5,9). Hence, find the coordinates of the points on this line which are at a distance of 14 units from point B.

Find the image A' of the point $A(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$. Also, find the equation of the line joining A and A'.

The angle which the line \(\frac{x}{1}=\frac{y}{-1}=\frac{z}{0}\) makes with the positive direction of Y-axis is: