Question

Find the dot product of vectors a and b and the angle between them. a = (9,0) b = (5,8)

Answer 1

57.99 degrees

Explanation:

a = <9, 0> and b = <5, 8>.

Then the dot product is (9)(5) + (0)(8) = 45 (a scalar)

The cosine of the angle between these two vectors is

a · b 45 45 5

cos Ф = --------- = ------------------------ = ------------- = -------- = 0.53

|a||b| (9)( √[25 + 64] ) 9(√89) √89

The angle between the vectors is arccos 0.53, which comes out to 1.01 radian or 57.99 degrees.