Question

已知向量a＝(4,5cosα),b＝(3,-4tanα),α∈(0,π/2),若a⊥b,一,求：|a+b|.二,求cos

Answer 1

a⊥b

则ab=0 得：12-20sina=0

即：sina=3/5

又有α∈(0,π/2) ,所以：cosa=4/5

|a+b|^2

=a^2+2ab+b^2

=50

所以：|a+b|=5√2

2、cos(a+π/4)

=cosasinπ/4+sinacosπ/4

=7√2/10