Find the angle between the lines whose direction ratios are:

2, -3, 4 and 1, 2, 1.


The angle between the two lines is given by


cos =


where R1 and R2 denote the vectors with the direction ratios,


So, here we have,


R1 = 2i - 3j + 4k and R2 = i +2j + k


cos =


cos


Hence,


1