The correct option is A 4150
We know that If two lines with direction cosines l1,m1,n1 and l2,m2,n2 intersect then the angle between them would be cos−1(l1.l2+m1.m2+n1.n2) Here we are given direction ratios and not the direction cosines. So we’ll find direction cosines first.
Direction cosines for the first line will be -
5√52+72+32,7√52+72+32,3√52+72+32
Or, 5√83,7√83,3√83
Similarly, direction cosines for the second line will be -
3√32+42+52,4√32+42+52,5√32+42+52
Or, 3√50,4√50,5√50
Now we can calculate the angle between these lines, which will be -
cos−1(5√83.3√50+7√83.4√50+3√83.5√50)
Or, cos−1(58√4150)
On comparing it with the given expression we get b = 4150