<p>The projection of a line segment on the coordinate axes are 2, 3, 6. Then, the length of the line segment is</p>
Step-by-Step Solution
Key Concept: The projections of a line segment on the axes are the products of direction cosines and the length, and the sum of squares of direction cosines equals 1.
Step 1: Let the length of the line segment be \(r\) and its direction cosines be \(l, m, n\). The projections on coordinate axes are \(lr, mr, nr\). Step 2: Given: \(lr = 2, mr = 3, nr = 6\) Step 3: Therefore, \(l^2r^2 + m^2r^2 + n^2r^2 = 4 + 9 + 36\) Step 4: \(r^2(l^2 + m^2 + n^2) = 49\) Step 5: Since \(l^2 + m^2 + n^2 = 1\), we have \(r^2 = 49\) \(∴ r = 7\) Answer is (a).
Correct Answer: A