u 8j and v isquare root of 3 j Find u times v and find the a

u= -8j and v= -i-square root of 3 j Find u times v and find the angle between u and v to the nearest degree

Solution

u= -8j

v= -i - 3 j

IuI = 8

IvI = sqrt[1 + 3] = 2

u.v = -8j.( -i - 3 j ) = 83

Now u.v = IuI*IvI*cos(theta)

83 = 8*2*cos(theta)

cos(theta) = 3/2

(theta) = 30 degree