JEE Class main Answered

If the direction ratio of line is (a, b, c) then its direction cosine is ( a/r, b/r, c/r  ),  where r = [ a² + b² + c² ]^1/2

If the direction ratio of line is (1,-2, 1) then its direction cosine is ( 1/√6 , -2/√6 , 1/√6 ) ;

If the direction ratio of line is (4,3,2) then its direction cosine is ( 4/√(29) , 3/√(29) , 2/√(29) ) ;

If ( l1 , m1, n1 ) is direction cosine of a line and (l2, m2, n2) is direction cosine of another line , then angle θ between two lines is

Hence angle θ between two given lines is calculated as

hence angle θ = 90