Projection of a Line Segment on a Line

Q. The projection of the line segment joining the points (–1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3 is

1. $\frac{10}{7}$
2. $\frac{22}{7}$
3. $\frac{18}{7}$
4. $5$

Q. The coordinates of the point equidistant from the points (a, 0, 0), (0, a, 0), (0, 0, a) and (0, 0, 0) are

1. $(\frac{a}{3},\frac{a}{3},\frac{a}{3})$
2. $(\frac{a}{2},\frac{a}{2},\frac{a}{2})$
3. $(a,a,a)$
4. $(2a,2a,2a)$

Q. The distance between two points P and Q is d and the length of their projections of PQ on the coordinate planes are $d_1,d_2,d_3$. Then ​$d_1^2+d_2^2+d_3^2=k{d}^2$, where k is

1. 1
2. 5
3. 3
4. 2