Question

设A向量＝（4,-3）B向量＝（2,1）若A向量+tB向量与B向量的夹角为45度,求实数t

Answer 1

a+tb=(4+2t,-3+t)

(a+tb)*b=2(4+2t)+(-3+t)=5+5t

又有(a+tb)*b=|a+tb||b|cos45

5+5t=根号[(4+2t)^2+(-3+t)^2]*根号(4+1)*根号2/2

25+50t+25t^2=(16+16t+4t^2+9-6t+t^2)*5/2

10+20t+10t^2=5t^2+10t+25

5t^2+10t-15=0

t^2+2t-3=0

(t+3)(t-1)=0

t=-3或t=1