If the projections of a straight line segment on the coordinate axes are 2, 3, 6, then the length of the segment is

Concept:

The direction cosines of the vector is the corresponding coordinate of vector divided by the length of the vector. 

If l, m, and n are direction cosines,then l2 + m2 + n2 = 1

Calculation:

The projections of a straight line segment on the coordinate axes are 2, 3, 6

Let, l, m, and n be the direction cosines of given line and k is the length of a straight line

So, l = 2/k ⇒ lk = 2

m = 3/k ⇒ mk = 3

n = 6/k ⇒ nk = 6

Now,

\(\rm (lk)^2+(mk)^2+(nk)^2 =2^2+3^2 +6^2 \\ \Rightarrow (l^2+m^2+n^2)k^2=4+9+36 \\\Rightarrow (1)k^2=49\cdots(\because l^2+m^2+n^2=1) \\\Rightarrow k = 7\)

Hence, option (2) is correct.