Question

已知向量lal=6lbl=6√2.若ta+b与ta-b夹角钝角,则t取值范围

Answer 1

设向量a=(x1,y1),向量b=(x2,y2)

x1^2+y1^2=36

x2^2+y2^2=72

(ta+b)·(ta-b)=(tx1+x2)(tx1-x2)+(ty1+y2)(ty1-y2)=36*t^2-72=36(t^2-2)