Question

设e1,e2是互相垂直的两个单位向量,a=3e1+4e2,b=-3e1+4e2,那么a与b的夹角---

Answer 1

e1,e2互相垂直

则e1*e2=0

a=3e1+4e2

两边平方

|a|^2=9|e1|^2+16|e2|^2+24e1*e2

|a|^2=9+16

|a|=5

同理可知|b|=5

a*b

=(3e1+4e2)*(-3e1+4e2)

=-9|e1|^2+16|e2|^2

=16-9

=7

a与b的夹角θ

cosθ=a*b/[|a|*|b|]=7/25

θ=arccos7/25