Question

已知向量a=(3,-2),向量b=(-1,0),求

Answer 1

|a|=√13.

向量a-向量2b=(3,-2)-2(-1,0).

=(3+2,-2-0).

=(5,-2).

|向量a-2向量b|=√29.

向量a.向量a-2向量b=3*5+(-2)*(-2).

=19.

cos＜向量a,向量a-2向量b＞=(向量a.向量2b)/|a||a-2b|.

=19/(√13*√29).

=19*√377/(13*29).

=368.9133/377.

=0.9785

∴＜向量a,向量a-2向量b＞≈11.89°