设单位向量c=(cosα.sinα) 0 ∵向量a∥向量c,∴3*sinα-4cosα=0.
3tanα-4=0.
tanα=4/3.
sec^2α=1+tan^2α.
=1+(4/3)^2.
=25/9.
secα=5/3.
cosα=1/secα=3/5.
sinα=√(1-cos^2α).
=4/5.
∴单位向量c的坐标为c=(3/5,4/5).
若向量|b|=√5.(|a|=5).
∵ 向量(a-2b)⊥向量（2a-b).
∴(a-2b).(2a-b)=0.
即,2a^2-5ab+2b^2=0.
a^2-5|a||b|cos
+2b^2=0.
cos
=(a^2+2b^2)/(5*|a||b|).
=25+2*5)/(5*5√5).
=35√5/125.
=7√5/25. ----即为所求.