Question

已知点O（0,0），A（1,2），B（4,5）及向量OP=向量OA+t倍向量AB

四边形OABP是否能成为平行四边形？若能，则求出t的值，若不能，说明理由
求解释，谢谢

Answer 1

OA = (1,2)
PB
= OB - OP
= OB - OA-tAB
=(4,5) - (1,2) - t(3,3)
=(3-3t, 3-3t)
ifOABP是平行四边形
=>OA = PB
=> (1,2) = (3-3t, 3-3t)
=> 1 = 3-3t and 2=3-3t
no such t exists
=>OABP不是平行四边形