Question

几道高一数学向量题

1.在平行四边形ABCD中，AC为对角线，若AB=(2，4) AC=(1，3) 则BD=? (过程)
2.若a=(1,2) b=(x,1) u=a+2b v=2a-b 且u⊥v 求x的值 (过程)

Answer 1

1. BD = AD - AB (向量的平行四边形加法法则:AC = AB + AD)
= (AC - AB) - AB
= AC - 2AB
= (1, 3) - 2(2, 4)
= (-3, -5)

2. u = a + 2b
= (1, 2) + 2(x, 1)
= (1+2x, 4)

v = 2a - b
= 2(1, 2) - (x, 1)
= (2-x, 3)

∵u⊥v, ∴u•v = 0
即(1+2x, 4)•(2-x, 3) = 0
(1+2x)(2-x) + 4*3 = 0
化简得 2x² - 3x - 14 = 0
(x + 2)(2x - 7) = 0
解得x = -2 或 x = 7/2