The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason( R)'. You are to axamine these two statements carefully and select the answer.
Assertion (A) : If lt l, m, n gt are direction cosines of a line, there can be a line whose direction cosines are
`(sqrt((l^2+m^2)/2),sqrt((m^2+n^2)/2),sqrt((n^2+l^2)/2),)`.
Reason(R) : The sum of direction cosines of a line is unity.

Options

A. Both A and R individually true, and R is the correct explanation of A.
B. Both A and R are individually true but R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.

Answer

C

Explanation

Sum of directions cosines of a line i.e., `l+m+n ne1`.
So, R is false.
Since sum of square of direction cosines is unity
`(sqrt((l^2+m^2)/2))^2+(sqrt((m^2+n^2)/2))^2+(sqrt((n^2+l^2)/2))^2`
`(l^2+m^2)/2+(m^2+n^2)/2+(n^2+l^2)/2`
`rArr(2(l^2+m^2+n^2))/2=l^2+m^2+n^2=1`
Hence, assertion A is ture.
So, A is true but R is false.