Q. If are the direction ratios of a line and are the direction cosines of the line, then

 971  162 Three Dimensional Geometry Report Error

Solution:

Let and be direction ratios of a line and and be the direction cosines (DC's) of the line.
Then, (say), being a constant.
Therefore, ...(i)
But
Therefore,
or
Hence, from Eq. (i), the DC's of the line are


where, depending on the desired sign of , either a positive or a negative sign is to be taken for and .