Question

已知向量a,b满足:|a|=4,|b|=3,且（2a+3b）点乘（2a-b）=61. 1：求a点乘b的值 2：求向量a与

Answer 1

(1)

(2a+3b)*(2a-b)

=4a^2-2ab+6ab-3b^2

=4|a|^2+4ab-3|b|^2

=4*4^2+4ab-3*3^2

=37+4ab=61

ab=6

(2)

cos(a,b)=a*b/|a|*|b|

=6/(4*3)

=1/2

所以角=60°

(3)

|a-b|=√(a-b)^2=√(a^2-2ab+b^2)=√(|a|^2+|b|^2-2ab)=√(4^2+3^2-2*6)=√13