The problem requires finding the length of a line given its projections on the coordinate axes. To solve this, we can use the formula for the length of a line segment with projections on the coordinate axes. The projections of a line on the axes are analogous to its direction ratios.
Given projections on the coordinate axes:
The formula for the length of the line using its projections (direction ratios) is:
\(L = \sqrt{a^2 + b^2 + c^2}\)
Substituting the given values into the formula:
\(L = \sqrt{2^2 + 3^2 + 6^2}\)
\(L = \sqrt{4 + 9 + 36}\)
\(L = \sqrt{49}\)
\(L = 7\)
Thus, the length of the line is 7.