find the angle between the given vectors aij b4i3jSolutionai

find the angle between the given vectors

a=i+j, b=4i-3j

Solution

a=i+j   ,    b= 4i -3j

magnitude of vector a, I a I=sqrt(1²+1²) = sqrt2

magnitude of vectot b , I b I= sqrt(4²+(-3)²) =5

vector a . vector b= 1*4 +1*(-3)= 1

cos theta= vector a.vector b/I a I I b I = 1/5sqrt2

theta=cos^-1(1/5sqrt2) =81.9 degree