Hello Aspirant

To find angle between two given vectors, we always use the dot product.

The dot product of two vectors is written as:

vector a.vector b = (mod of vector a)*(mod of vector b)*cos(theeta)

Now, a = 3icap + 4jcap, b = 12icap + 5jcap

So, we get vector a. vector b =  (3icap + 4jcap)*(12icap + 5jcap) = 36 + 20 = 56

Also, mod of a = square root(9 + 16) = 5

mod of b = square root(144 + 25) = 13

So, we get 56 = 13*5*cos(theeta)

cos(theeta) = 56/65

theeta = cos - inverse(56/65)

So, the angle between given vectors is cos - inverse(56/65).