Question

设向量a+b=(16,-8)与向量a-b=(-8,2)求向量a与b夹角θ 的余弦

Answer 1

a+b=(16,-8) (1)

a-b=(-8,2) (2)

(1)+(2)

2a=(8,-6)

a=(4,-3)

(1)-(2)

b = (12,-5)

|a|=5

|b|=13

|a||b|cosθ =a.b

65cosθ = (4,-3).(12,-5)

=48+15

cosθ = 63/65