Question

已知向量a的模▏a▏=4,向量b的模▏b▏=5,向量a与b的夹角θ为π/3(要详细过程）

求(1)a*b(2) (a+b)^2 (3)a^2-b^2(4)(2a+3b)*(3a-2b)

Answer 1

1=4*5* cos60度=10
2=[a]向量平方加[b]向量平方加2[a]向量[b]向量*cos60度=16加25加20=61
3=（a+ b)^2-4a向量b向量=61^2-40=3681
4=6a^2-4ab+9ab-6b^2=6*4*4+5*10-6*25=44
a，b都表示向量哦！电脑没法输向量符号

Answer 2

(1) a*b=|a|*|b|*cos(π/3)=4×5×(1/2)=10
(2) (a+b)^2=a^2+2a*b+b^2=16+20+25=61
(3)a^2-b^2=|a|^2-|b|^2=16-25=-9
(4)(2a+3b)*(3a-2b)=6a^2+5a*b-6b^2=196+50-150=-4

Answer 3

(1)
a.b=|a||b|cosπ/3=4(5)(1/2) = 10
(2)
|a+b|^2=(a+b).(a+b) = |a|^2+|b|^2+2a.b = 16+25+2(10)= 61
(3)
|a|^2-|b|^2 = 16-25=-7
(4)
(2a+3b).(3a-2b)= 6|a|^2-6|b|^2+5a.b = 6(16)-6(25)+5(10)=-4

Answer 4

a.b=|a||b|cos<a,b>=4*5*1/2=10
(a+b)^2=|a|^2+|b|^2+2a.b=16+25+20=61
a^2-b^2=|a|^2-|b|^2=16-25=-9
(2a+3b).(3a-2b)=6|a|^2-6|b|^2+5a.b=6*(16-25)+5*10=50-54=-4