The projection of a line segment on the axis 2, 3, 6 respectively. Then find the length of line segment.

Options

A. 7
B. 5
C. 1
D. 11

Answer

A

Explanation

Let the length of the line segment be `r` and its direction cosines be `l,m,n`. Then its projections on the coordinate axes are `lr,mr,nr`.
`:.lr=2,mr=3` and `nr=6`
`impliesl^(2)r^(2)+m^(2)r^(2)+n^(2)r^(2)=4+9+36`
`implies r^(2)(l^(2)+m^(2)n^(2))=49`
`impliesr^(2)=49impliesr=7 [ :' l^(2)+m^(2)+n^(2)=1]`