Consider the following u i 5j v 6i j Find u middot v u m

Consider the following. u = i + 5j, v = 6i - j Find u middot v. u middot v = Find the angle between u and v to the nearest degree. theta = degree

Solution

u = i + 5j

v = 6i - j

a) u.v = (1*6) + (5*-1) = 6 - 5 = 1

b) IuI = sqrt(26)

IvI = sqrt(37)

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

1 = sqrt(26*37)*cos(theta)

Theta = arccos[1/sqrt(26*37)] = 88.15 degree